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Subshift semigroupsAug 22 2019Given a one-sided subshift $X$ on a finite alphabet, we consider the semigroup $S_X =L_X \cup \{0\}$, where $L_X $ is the language of $X $, equipped with the multiplication operation given by concatenation, when allowed, and set to vanish otherwise. We ... More

Brown Measures of Free Circular and Multiplicative Brownian Motions with Probabilistic Initial PointAug 22 2019Given a selfadjoint random variable $x_0$ and a unitary random variable $u$, different from Haar unitary, free from the free circular Brownian motion $c_t$ and the free multiplicative Brownian motion $b_t$, we use the Hamilton-Jacobi method to compute ... More

Quasi-local Algebras and Asymptotic ExpandersAug 21 2019In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a discrete metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic ... More

Stationary characters on lattices of semisimple Lie groupsAug 21 2019We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications in representation theory, operator ... More

Quantum Euclidean Spaces with Noncommutative DerivativesAug 21 2019Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical commutation relation ... More

Noncommutative Cartan C*-subalgebrasAug 20 2019We characterise Exel's noncommutative Cartan subalgebras in several ways using uniqueness of conditional expectations, relative commutants, or purely outer inverse semigroup actions. We describe in which sense the crossed product decomposition for a noncommutative ... More

Character rigidity of simple algebraic groupsAug 19 2019We prove the following extension of Tits' simplicity theorem. Let $k$ be an infinite field, $G$ an algebraic group defined and quasi-simple over $k,$ and $G(k)$ the group of $k$-rational points of $G.$ Let $G(k)^+$ be the subgroup of $G(k)$ generated ... More

On some conjectures by Lu and WenzelAug 19 2019In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward several new conjectures ... More

The Cuntz semigroup and the radius of comparison of the crossed product by a finite groupAug 17 2019Let G be a finite group, let A be an infinite-dimensional stably finite simple unital C*-algebra, and let \alpha \colon G \to Aut (A) be an action of G on A which has the weak tracial Rokhlin property. Let A^{\alpha} be the fixed point algebra. Then the ... More

Classification of tensor decompositions for II$_1$ factorsAug 17 2019In the mid thirties Murray and von Neumann found a natural way to associate a von Neumann algebra $L(\Gamma)$ to any countable discrete group $\Gamma$. Classifying $L(\Gamma)$ in term of $\Gamma$ is a notoriously complex problem as in general the initial ... More

Partial generalized crossed products and a seven-term exact sequenceAug 16 2019For a partial Galois extension of commutative rings we give a seven term exact sequence which generalize the Chase-Harrison-Rosenberg sequence.

Additive Local Multiplications and zero-preserving maps on $C(X)$Aug 15 2019Suppose $X$ is a compact Hausdorff space. In terms of topolocical properties of $X$, we find topological conditions on $X$ that are equivalent to each of the following: 1. every additive local multiplication on $C\left( X\right) $ is a multiplication, ... More

Fourier transform, Schrödinger representation, and Heisenberg modulesAug 13 2019We investigate and review how Fourier transform is involved in the analysis of a twisted group algebra $L^1(G, \sigma)$ for $G=\widehat{\Gamma}\times \Gamma$ and $\sigma:G\times G \to \mathbb{T}$ 2- cocycle where $\Gamma$ is a locally compact abelian ... More

Structure of block quantum dynamical semigroups and their product systemsAug 12 2019W. Paschke's version of Stinespring's theorem associates a Hilbert $C^*$-module along with a generating vector to every completely positive map. Building on this, to every quantum dynamical semigroup (QDS) on a $C^*$-algebra $\mathcal A$ one may associate ... More

Matrix-analytic solution of system of integral equations in three tandem serversAug 12 2019A matrix-analytic method is proposed for solving a system of linear integral equations arises in three tandem servers. The approach is by modelling the cumulative distribution function (cdf) of the service time as a matrix exponential function. The method ... More

Inductive limits of compact quantum groups and their unitary representationsAug 12 2019We will introduce the notion of inductive limits of compact quantum groups as $W^*$-bialgebras equipped with some additional structures. We also formulate their unitary representation theories. Those give a more explicit representation-theoretic meaning ... More

Bisynchronous Games and Factorizable MapsAug 11 2019We introduce a new class of non-local games, and corresponding densities, which we call bisynchronous. Bisynchronous games are a subclass of synchronous games and exhibit many interesting symmetries when the algebra of the game is considered. We develop ... More

Groups with Spanier-Whitehead dualityAug 10 2019We introduce the notion of Spanier-Whitehead K-duality for a discrete group G, defined as duality in the KK-category between two C*-algebras which are naturally attached to the group, namely the reduced group C*-algebra and the crossed product for the ... More

Refined moves for structure-preserving isomorphism of graph C*-algebrasAug 10 2019We formalize eight different notions of isomorphism among (unital) graph C*-algebras, and initiate the study of which of these notions may be described geometrically as generated by moves. We propose a list of seven types of moves that we conjecture has ... More

2-positive almost order zero maps and decomposition rankAug 09 2019We consider 2-positive almost order zero (disjointness preserving) maps on C*-algebras. Generalizing the argument of M. Choi for multiplicative domains, we give an internal characterization of almost order zero for 2-positive maps. It is also shown that ... More

Non-amenable tight squeezes by Kirchberg algebrasAug 08 2019We provide a constructive ambient Kirchberg algebra of the reduced free group C*-algebra ${\mathrm C}^\ast_{\mathrm r}(\mathbb{F}_\infty)$ without intermediate C*-algebras. Moreover we show that every Kirchberg algebra is KK-equivalently sandwiched by ... More

A non-nuclear $C^*$-algebra with the Weak Expectation Property and the Local Lifting PropertyAug 07 2019We construct a non-exact $C^*$-algebra $A$ with both the Weak Expectation Property (WEP) and the Local Lifting Property (LLP). This gives a new example of non-nuclear $A$ for which there is a unique $C^*$-norm on $A \otimes A^{op}$. This example is of ... More

Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modulesAug 07 2019We associate to each Temperley-Lieb-Jones C*-tensor category $\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ with parameter $\delta$ in the discrete range $\{2\cos(\pi/(k+2))\,:\,k=1,2,\ldots\}\cup\{2\}$ a certain C*-algebra $\mathcal{B}$ of compact operators. ... More

Controlled Analytic Properties and the Quantitative Baum-Connes ConjectureAug 06 2019We show that the classical Baum-Connes assembly map is quantitatively an isomorphism for a class of lacunary hyperbolic groups, and we explain how to see that this class contains many examples of groups that contain graph sequences of large girth inside ... More

Factorizations of Schur functionsAug 05 2019The Schur class, denoted by $\mathcal{S}(\mathbb{D})$, is the set of all functions analytic and bounded by one in modulus in the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$, that is \[ \mathcal{S}(\mathbb{D}) = \{\varphi \in H^\infty(\mathbb{D}): ... More

A Groupoid Picture of Elek AlgebrasAug 04 2019We describe a construction by G\'abor Elek, associating C*-algebras with uniformly recurrent subgroups, in the language of groupoid C*-algebras. This allows us to simplify several proofs in the original paper and fully characterise their nuclearity. We ... More

Decomposing nuclear mapsAug 02 2019We show that the strengthened version of the completely positive approximation property of Brown, Carri\'on, and White---where the downward maps are asymptotically order zero and the upward maps are convex combinations of order zero maps---is enjoyed ... More

Classification of tiling $C^*$-algebrasAug 02 2019We prove that Kellendonk's $C^*$-algebra of an aperiodic and repetitive tiling with finite local complexity is classifiable by the Elliott invariant. Our result follows from showing that Kellendonk's tiling $C^*$-algebras are $\mathcal{Z}$-stable, and ... More

Polynomials on cyclic monotone elements with applications to random matrices with discrete spectrumAug 01 2019We provide a generalization and new proofs of the formulas of Collins, Hasebe and Sakuma for the spectrum of polynomials in cyclic monotone elements. This is applied to random matrices with discrete spectrum.

Pointwise convergence of noncommutative Fourier seriesAug 01 2019This paper is devoted to the study of convergence of Fourier series for non-abelian groups and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as some summation methods and mean convergence of associated ... More

CCR and CAR flows over convex conesAug 01 2019Recently it is proved in arXiv:1906.05493v1 [math.OA] that CCR flows over convex cones are cocycle conjugate if and only if the associated isometric representations are conjugate. We provide a very short, simple and direct proof of that. Using the same ... More

Noncommutative weak $(1,1)$ type estimate for a square function from ergodic theoryJul 31 2019In this paper, we investigate the boundedness of a square function from ergodic theory on noncommutative $L_{p}$-spaces. The main result is a weak $(1,1)$ type estimate of this square function. We also show the $(L_{\infty},\mathrm{BMO})$ estimate, and ... More

Non-Fermi Liquid Behaviors in the Hubbard model on the Honeycomb latticeJul 29 2019Aug 11 2019In this paper we study the low temperature ($T\rightarrow 0$) behaviors of the weakly interacting Hubbard model on the honeycomb lattice with a bare chemical potential, which takes values in a small neighborhood of the renormalized chemical potential ... More

Non-Fermi Liquid Behaviors in the Hubbard model on the Honeycomb latticeJul 29 2019In this paper we study the weakly interacting Hubbard model on the honeycomb lattice with a bare chemical potential, which takes values in a $\epsilon_{\lambda}$-neighborhood of the renormalized chemical potential $\mu$, whose value is fixed to be $1$, ... More

Maximal ergodic inequalities for some positive operators on noncommutative $l^p$-spacesJul 29 2019In this paper, we establish one-sided maximal ergodic inequalities for a large class of positive operators on noncommutative $L^p$-space which do not fall into the category of positive contractions considered by Junge and Xu. Our method partly relies ... More

A remark on matrix product operator algebras, anyons and subfactorsJul 29 2019We show that the mathematical structures in a recent work of Bultinck-Mari\"ena-Williamson-\c Sahino\u glu-Haegemana-Verstraete are the same as those of flat symmetric bi-unitary connections and the tube algebra in subfactor theory. More specifically, ... More

Conditioning of Quantum Open SystemsJul 27 2019The underlying probabilistic theory for quantum mechanics is non-Kolmogorovian. The order in which physical observables will be important if they are incompatible (non-commuting). In particular, the notion of conditioning needs to be handled with care ... More

A Guide to the Bott Index and Localizer IndexJul 26 2019The Bott index is inherently global. The pseudospectal index is inherently local, and so now the preferred name is the localizer index. We look at these on a rather standard model for a Chern insulator, with an emphasis how to program these effectively. ... More

Sandwich theorems and capacity bounds for non-commutative graphsJul 26 2019We define non-commutative versions of the vertex packing polytope, the theta convex body and the fractional vertex packing polytope of a graph, and establish a quantum version of the Sandwich Theorem of Gr\"{o}tschel, Lov\'{a}sz and Schrijver. We define ... More

Positive definite radial kernels on homogeneous trees and productsJul 26 2019We give a new proof of a classical result which provides a one-to-one correspondence between positive definite radial kernels on a homogeneous tree and finite Borel measures on the interval $[-1,1]$. Our methods allow us to find a new characterisation ... More

Boolean Cumulants and Subordination in Free ProbabilityJul 26 2019We study subordination of free convolutions. We prove that for free random variables $X,Y$ and a Borel function $f$ the conditional expectation $E_\varphi\left[ (z-X-f(X)Yf^*(X))^{-1}| X\right]$, is a resolvent again. This result allows explicit calculation ... More

Conditional expectations through Boolean cumulants and subordination -- towards a better understanding of the Lukacs property in free probabilityJul 25 2019We use here a recent idea of studying functions of free random variables using Boolean cumulants. We develop idea of explicit calculations of conditional expectation using Boolean cumulants. We demonstrate Boolean cumulants approach allows to calculate ... More

An operator-valued $T1$ theory for symmetric CZOsJul 25 2019We provide a natural BMO-criterion for the $L_2$-boundedness of Calder\'on-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix, we give a ... More

Angles between Haagerup--Schultz projections and spectrality of operatorsJul 24 2019We investigate angles between Haagerup--Schultz projections of operators belonging to finite von Neumann algebras, in connection with a property analogous to Dunford's notion of spectrality of operators. In particular, we show that an operator can be ... More

On pointwise products of symmetric quasi Banach spaces and applicationsJul 24 2019Let $E_1,\;E_2$ be symmetric quasi Banach spaces on $[0,\alpha)\;(0<\alpha\le\8)$. We collected and proved some properties of the space $E_1\odot E_2$, where $\odot$ means the pointwise product of symmetric quasi Banach spaces. Under some natural assumptions, ... More

Coarse Baum-Connes conjecture and rigidity for Roe algebrasJul 24 2019In this paper, we connect the rigidity problem and the coarse Baum-Connes conjecture for Roe algebras. In particular, we show that if $X$ and $Y$ are two uniformly locally finite metric spaces such that their Roe algebras are $*$-isomorphic, then $X$ ... More

The Riemann-Roch Theorem on higher dimensional complex noncommutative toriJul 24 2019We prove analogues of the Riemann-Roch Theorem and the Hodge Theorem for noncommutative tori (of any dimension) equipped with complex structures, and discuss implications for the question of how to distinguish "noncommutative abelian varieties" from "non-algebraic" ... More

Equivariant Dimensions of Graph C*-algebrasJul 23 2019We explore the recently introduced local-triviality dimensions by studying gauge actions on graph $C^*$-algebras, as well as the restrictions of the gauge action to finite cyclic subgroups. For $C^*$-algebras of finite acyclic graphs and finite cycles, ... More

Fermionic Topological Order on TriangulationsJul 23 2019Fermion models belong to the CAR algebra. Following Kitaev's work on toric models, we identify a sub-algebra of CAR, generated by elements associated with the triangles and vertices of a finite triangulation of a surface $M$ of genus $g$. We show that ... More

Fermionic Topological Order on TriangulationsJul 23 2019Jul 24 2019Fermionic physical models belong to the CAR algebra. Following Kitaev's work on toric models, we identify a sub-algebra of CAR, generated by elements associated with the triangles and vertices of a finite triangulation of a surface $M$ of genus $g$. We ... More

The Distance from a Rank $n-1$ Projection to the Nilpotent Operators on $\mathbb{C}^n$Jul 22 2019Jul 24 2019Building on MacDonald's formula for the distance from a rank-one projection to the set of nilpotents in $\mathbb{M}_n(\mathbb{C})$, we prove that the distance from a rank $n-1$ projection to the set of nilpotents in $\mathbb{M}_n(\mathbb{C})$ is $\frac{1}{2}\sec\left(\frac{\pi}{\frac{n}{n-1}+2}\right)$. ... More

Non-commutative disintegrations: existence and uniqueness in finite dimensionsJul 22 2019We utilize category theory to define non-commutative disintegrations, regular conditional probabilities, and optimal hypotheses for finite-dimensional C*-algebras. In the process, we introduce a notion of a.e. equivalence for positive maps and show that ... More

Smooth Connes--Thom isomorphism, cyclic homology, and equivariant quantisationJul 21 2019Using a smooth version of the Connes--Thom isomorphism in Grensing's bivariant K-theory for locally convex algebras, we prove an equivariant version of the Connes--Thom isomorphism in periodic cyclic homology. As an application, we prove that periodic ... More

Exactness vs C*-exactness for certain non-discrete groupsJul 20 2019It is known that exactness for a discrete group $G$ is equivalent to C*-exactness, i.e., the exactness of the reduced C*-algebra. The problem of whether this equivalence holds for general locally compact groups has recently been reduced by Cave and Zacharias ... More

Theory of $B(X)$-moduleJul 20 2019In this Lecture Note the theory of $B(X)$-module is explained at first. In the latter part of each section the utility of the theory is confirmed in the application to the abstract Cauchy problem, the Cole-Hopf transform, and the rotation group.

New products and $\mathbb{Z}_2$-extensions of compact matrix quantum groupsJul 19 2019There are two very natural products of compact matrix quantum groups: the tensor product $G\times H$ and the free product $G*H$. We define a number of further products interpolating these two. We focus more in detail to the case where $G$ is an easy quantum ... More

A note on the classification of Gamma factorsJul 18 2019One of the earliest invariants introduced in the study of finite von Neumann algebras is the property Gamma of Murray and von Neumann. In this note we prove that it is not possible to classify separable $\rm{II}_1$ factors satisfying the property Gamma ... More

Superadditivity of the regularized Minimum Output EntropyJul 18 2019The problem of additivity of the Minimum Output Entropy is of fundamental importance in Quantum Information Theory. It was solved by Hastings in 2009 in the one-shot case, by exhibiting a pair of super-additive channels. The purpose of this paper is to ... More

Representing some II$_1$ factors in $L^2(Λ\backslash G)$Jul 17 2019Let $G$ be $PGL(n,F)$, $n \geq 3$, $F$ a certain non-archimedean local field; or let $G$ be $PSL(2,\mathbb{R}) \times \cdots \times PSL(2,\mathbb{R})$. Let $\Gamma$ be a lattice in $G$, and let $( \Lambda_n )$ be a sequence of lattices in $G$ satisfying ... More

Algebraic Calderón-Zygmund theoryJul 17 2019Calder\'on-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general measure spaces which admit a Markov semigroup satisfying ... More

Quantum metrics on the tensor product of a commutative C*-algebra and an AF C*-algebraJul 17 2019Given a compact metric space X and a unital AF algebra A equipped with a faithful tracial state, we place quantum metrics on the tensor product of C(X) and A given established quantum metrics on C(X) and A from work with Bice and Latr\'emoli\`ere. We ... More

Fixed points and limits of convolution powers of contractive quantum measuresJul 17 2019We study fixed points of contractive convolution operators associated to contractive quantum measures on locally compact quantum groups. We characterise the existence of non-zero fixed points respectively on $L^\infty(\mathbb{G})$ and on $C_0(\mathbb{G})$, ... More

Isometries on non-commutative (quantum) Lorentz spaces associated with semi-finite von Neumann algebrasJul 16 2019In this article we characterize the extreme points of the unit ball of a non-commutative (quantum) Lorentz space associated with a semi-finite von Neumann algebra. This enables us to show that surjective isometries between non-commutative Lorentz spaces ... More

On Cyclic Finite-State Approximation of Data-Driven SystemsJul 15 2019Jul 18 2019In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix approximation problems ... More

On Cyclic Finite-State Approximation of Data-Driven SystemsJul 15 2019In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for these techniques came from structure-preserving matrix approximation problems, that appear in ... More

Isometries between non-commutative symmetric spaces associated with semi-finite von Neumann algebrasJul 15 2019In this article we show that positive surjective isometries between symmetric spaces associated with semi-finite von Neumann algebras are projection disjointness preserving if they are finiteness preserving. This is subsequently used to obtain a structural ... More

Cotangent bundles for "matrix algebras converge to the sphere''Jul 14 2019In the high-energy quantum-physics literature one finds statements such as ``matrix algebras converge to the sphere''. Earlier I provided a general setting for understanding such statements, in which the matrix algebras are viewed as compact quantum metric ... More

On a Characterization of the Weak Expectation Property (WEP)Jul 14 2019We give a detailed proof of a new characterization of the Weak Expectation Property (WEP) announced by Haagerup in the 1990's but unavailable (in any form) till now. Our main result is motivated by a well known conjecture of Kirchberg, which is equivalent ... More

On a Characterization of the Weak Expectation Property (WEP)Jul 14 2019Jul 23 2019We give a detailed proof of a new characterization of the Weak Expectation Property (WEP) announced by Haagerup in the 1990's but unavailable (in any form) till now. Our main result is motivated by a well known conjecture of Kirchberg, which is equivalent ... More

Primitive Ideals of Labelled Graph $C^*$-algebrasJul 14 2019Given a directed graph $E$ and a labeling $\mathcal{L}$, one forms the labelled graph $C^*$-algebra by taking a weakly left--resolving labelled space $(E, \mathcal{L}, \mathcal{B})$ and considering a universal generating family of partial isometries and ... More

Skew products of finitely aligned left cancellative small categories and Cuntz-Krieger algebrasJul 12 2019Given a group cocycle on a finitely aligned left cancellative small category (LCSC) we investigate the associated skew product category and its Cuntz-Krieger algebra, which we describe as the crossed product of the Cuntz-Krieger algebra of the original ... More

The royal road to automatic noncommutative real analyticity, monotonicity, and convexityJul 12 2019It was shown classically that matrix monotone and matrix convex functions must be real analytic by L\"owner and Kraus respectively. Recently, various analogues have been found in several noncommuting variables. We develop a general framework for lifting ... More

A quantum metric on the Cantor SpaceJul 12 2019The first author and Latr\'emoli\`ere had introduced a quantum metric (in the sense of Rieffel) on the algebra of complex-valued continuous functions on the Cantor space. We show that this quantum metric is distinct from the quantum metric induced by ... More

An Introduction to Abstract Classification Theory in the Operator Algebraic SettingJul 12 2019In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the field of operator ... More

Fibered Cusp b-Pseudodifferential Operators and its ApplicationsJul 12 2019Let $X$ be a smooth compact manifold with corners which has two embedded boundary hypersurfaces $\partial_0 X , \partial_1 X$, and a fiber bundle $\phi:\partial_0 X \to Y$ is given. By using the method of blowing up, we define a pseudodifferential culculus ... More

Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approachJul 12 2019We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods. The latter are based on Hamiltonian lattice gauge theory and multi-scale analysis via inductive limits of $C^{*}$-algebras ... More

Commutant lifting and Nevanlinna-Pick interpolation in several variablesJul 11 2019This paper concerns a commutant lifting theorem and a Nevanlinna-Pick type interpolation result in the setting of multipliers from vector-valued Drury-Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over the unit ball ... More

Lie groupoids, pseudodifferential calculus and index theoryJul 11 2019Alain Connes introduced the use of Lie groupoids in noncommutative geometry in his pioneering work on the index theory of foliations. In the present paper, we recall the basic notion involved: groupoids, their C*-algebras, their pseudodifferential calculus... ... More

Pure infiniteness and paradoxicality for graph $C^*$-algebrasJul 11 2019We obtain necessary and sufficient conditions for pure infiniteness of the path groupoid $C^*$-algebra of a row-finite graph without sinks. In particular we show that for such a path groupoid $\mathcal{G}_E$, the properties of being essential principal ... More

Kippenhahn's Theorem for joint numerical ranges and quantum statesJul 10 2019Kippenhahn's Theorem asserts that the numerical range of a matrix is the convex hull of a certain algebraic curve. Here, we show that the joint numerical range of finitely many hermitian matrices is similarly the convex hull of a semi-algebraic set. We ... More

Metric characterisation of unitaries in JB$^*$-algebrasJul 10 2019Let $M$ be a unital JB$^*$-algebra whose closed unit ball is denoted by $\mathcal{B}_M$. Let $\partial_e(\mathcal{B}_M)$ denote the set of all extreme points of $\mathcal{B}_M$. We prove that an element $u\in \partial_e(\mathcal{B}_M)$ is a unitary if ... More

The universal property of infinite direct sums in C$^*$-categories and W$^*$-categoriesJul 10 2019When formulating universal properties for objects in a dagger category, one usually expects a universal property to characterize the universal object up to unique unitary isomorphism. We observe that this is automatically the case in the important special ... More

Non-homogeneous extensions of Cantor minimal systemsJul 09 2019Floyd gave an example of a minimal dynamical system which was an extension of an odometer and the fibres of the associated factor map were either singletons or intervals. Gjerde and Johansen showed that the odometer could be replaced by any Cantor minimal ... More

Homotopy equivalence in unbounded KK-theoryJul 09 2019We propose a new notion of unbounded $K\!K$-cycle, mildly generalising unbounded Kasparov modules, for which the direct sum is well-defined. To a pair $(A,B)$ of $\sigma$-unital $C^{*}$-algebras, we can then associate a semigroup $\overline{U\!K\!K}(A,B)$ ... More

Homotopy equivalence in unbounded KK-theoryJul 09 2019Jul 23 2019We propose a new notion of unbounded $K\!K$-cycle, mildly generalising unbounded Kasparov modules, for which the direct sum is well-defined. To a pair $(A,B)$ of $\sigma$-unital $C^{*}$-algebras, we can then associate a semigroup $\overline{U\!K\!K}(A,B)$ ... More

$\ell^1$-contractive maps on noncommutative $L^p$-spacesJul 09 2019Let $T\colon L^p({\mathcal M})\to L^p({\mathcal N})$ be a bounded operator between two noncommutative $L^p$-spaces, $1\leq p<\infty$. We say that $T$ is $\ell^1$-bounded (resp. $\ell^1$-contractive) if $T\otimes I_{\ell^1}$ extends to a bounded (resp. ... More

Characterizing linear mappings through zero products or zero Jordan productsJul 09 2019Aug 08 2019Let $\mathcal{A}$ be a $*$-algebra and $\mathcal{M}$ be a $*$-$\mathcal A$-bimodule, we study the local properties of $*$-derivations, $*$-Jordan derivations, $*$-left derivations and $*$-Jordan left derivations from $\mathcal{A}$ into $\mathcal{M}$ under ... More

Characterizing linear mappings through zero products or zero Jordan productsJul 09 2019Let $\mathcal{A}$ be a unital $*$-algebra and $\mathcal{M}$ be a unital $*$-$\mathcal A$-bimodule, we study the local properties of $*$-derivations, $*$-Jordan derivations and $*$-left derivations from $\mathcal{A}$ into $\mathcal{M}$ through zero products ... More

Constructions in minimal amenable dynamics and applications to the classification of $\mathrm{C}^*$-algebrasJul 08 2019We study the existence of minimal dynamical systems, their orbit and minimal orbit-breaking equivalence relations, and their applications to C*-algebras and K-theory. We show that given any finite CW-complex there exists a space with the same K-theory ... More

Constructions in minimal amenable dynamics and applications to the classification of $\mathrm{C}^*$-algebrasJul 08 2019Jul 10 2019We study the existence of minimal dynamical systems, their orbit and minimal orbit-breaking equivalence relations, and their applications to C*-algebras and K-theory. We show that given any finite CW-complex there exists a space with the same K-theory ... More

Amenability and approximation properties for partial actions and Fell bundlesJul 08 2019Building on previous papers by Anantharaman-Delaroche we introduce and study the notion of AD-amenability for partial actions and Fell bundles over discrete groups. If the Fell bundle is AD-amenable, the full and reduced crossed products coincide. We ... More

One-parameter isometry groups and inclusions between operator algebrasJul 08 2019We make a careful study of one-parameter isometry groups on Banach spaces, and their associated analytic generators, as first studied by Cioranescu and Zsido. We pay particular attention to various, subtly different, constructions which have appeared ... More

The Realization Problem for Finitely Generated Refinement MonoidsJul 08 2019We show that every finitely generated conical refinement monoid can be represented as the monoid $\mathcal V(R)$ of isomorphism classes of finitely generated projective modules over a von Neumann regular ring $R$. To this end, we use the representation ... More

On ultraproduct embeddings and amenability for tracial von Neumann algebrasJul 07 2019Aug 01 2019We define the notion of \emph{self-tracial stability} for tracial von Neumann algebras and show that a tracial von Neumann algebra satisfying the Connes Embedding Problem is self-tracially stable if and only if it is amenable. We then generalize a result ... More

On ultraproduct embeddings and amenability for tracial von Neumann algebrasJul 07 2019We define the notion of \textit{self-tracial stability} for tracial von Neumann algebras and show that a tracial von Neumann algebra satisfying the Connes Embedding Problem is self-tracially stable if and only if it is amenable. We then generalize a result ... More

Regression conditions that characterizes free Poisson and free Kummer non-commutative random variablesJul 05 2019We find asymptotic spectral distribution of matrix--Kummer eigenvalues. Then we formulate and prove the free analogue of HV independence property, which is known for classical Kummer and Gamma random variables. We also prove related characterization of ... More

Rigidity and a common framework for mutually unbiased bases and k-netsJul 04 2019Many deep, mysterious connections have been observed between collections of mutually unbiased bases (MUBs) and combinatorial designs called $k$-nets (and in particular, between complete collections of MUBs and finite affine - or equivalently: finite projective ... More

Linear maps behaving like derivations or anti-derivations at orthogonal elements on C*-algebrasJul 04 2019Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and ab*=b*a=0. In each case, ... More

On a categorical framework for classifying C*-dynamics up to cocycle conjugacyJul 04 2019We provide the rigorous foundations for a categorical approach to the classification of C*-dynamics up to cocycle conjugacy. Given a locally compact group $G$, we consider a category of (twisted) $G$-C*-algebras, where morphisms between two objects are ... More

On a categorical framework for classifying C*-dynamics up to cocycle conjugacyJul 04 2019Jul 05 2019We provide the rigorous foundations for a categorical approach to the classification of C*-dynamics up to cocycle conjugacy. Given a locally compact group $G$, we consider a category of (twisted) $G$-C*-algebras, where morphisms between two objects are ... More