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Hölder classes via semigroups and Riesz transformsApr 23 2019We define H\"older classes $\Lambda_\alpha$ associated with a Markovian semigroup and prove that, when the semigroup satisfies the $\Gamma^2 \geq 0$ condition, the Riesz transforms are bounded between the H\"older classes. As a consequence, this bound ... More
The Furstenberg Boundary of a GroupoidApr 22 2019We define the Furstenberg boundary of a locally compact Hausdorff \'etale groupoid, generalising the Furstenberg boundary for discrete groups, by providing a construction of a groupoid-equivariant injective envelope.
Finite dimensional approximations for Nica-Pimsner algebrasApr 22 2019We give necessary and sufficient conditions for nuclearity of Cuntz-Nica-Pimsner algebras for a variety of quasi-lattice ordered groups. First we deal with the free abelian lattice case. We use this as a stepping stone to tackle product systems over quasi-lattices ... More
Invariant measures for Cantor dynamical systemsApr 21 2019This paper is a survey devoted to the study of probability and infinite ergodic invariant measures for aperiodic homeomorphisms of a Cantor set. We focus mostly on the cases when a homeomorphism has either a unique ergodic invariant measure or finitely ... More
E$_0$-semigroups and product systems of W$^*$-bimodulesApr 20 2019Product systems have been originally introduced to classify E$_0$-semigroups on type I factors by Arveson. We develop the classification theory of E$_0$-semigroups on a general von Neumann algebra and the dilation theory of CP$_0$-semigroups in terms ... More
The C*-algebra of the semi-direct product K and AApr 19 2019Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of $G $, generalizing ... More
Positivity of $2\times 2$ block matrices of operatorsApr 18 2019We review some of the significant generalizations and applications of the celebrated Douglas theorem on the equivalence of factorization, range inclusion, and majorization of operators. We then apply it to find a characterization of the positivity of ... More
A short proof of Thoma's theorem on type I groupsApr 16 2019In the theory of unitary group representations, a group is called type I if all factor representations are of type I, and by a celebrated theorem of James Glimm [Gli61b], the type I groups are precisely those groups for which the irreducible unitary representations ... More
Classifying (Weak) Coideal Subalgebras of Weak Hopf C*-AlgebrasApr 16 2019We develop a general approach to the problem of classification of weak coideal C*-subalgebras of weak Hopf C*-algebras. As an example, we consider weak Hopf C*-algebras and their weak coideal C*-subalgebras associated with Tambara Yamagami categories. ... More
All classifiable Kirchberg algebras are $C^{\ast}$-algebras of ample groupoidsApr 16 2019In this note we show that every Kirchberg algebra in the UCT class is the $C^{\ast}$-algebra of a Hausdorff, ample, amenable and locally contracting groupoid. The non-unital case follows from Spielberg's graph-based models for Kirchberg algebras. Our ... More
Matrix Algebras with a Certain Compression Property IIApr 16 2019A subalgebra $\mathcal{A}$ of $\mathbb{M}_n(\mathbb{C})$ is said to be projection compressible if $P\mathcal{A}P$ is an algebra for all orthogonal projections $P\in\mathbb{M}_n(\mathbb{C})$. Likewise, $\mathcal{A}$ is said to be idempotent compressible ... More
Embeddings of uniform Roe algebrasApr 15 2019In this paper, we study embeddings of uniform Roe algebras. Generally speaking, given metric spaces $X$ and $Y$, we are interested in which large scale geometric properties are stable under embedding of the uniform Roe algebra of $X$ into the uniform ... More
Quantum increasing sequences generate quantum permutation groupsApr 15 2019We answer a question of A. Skalski and P.M. So{\l}tan (2016) about inner faithfulness of the S.~Curran's map of extending a quantum increasing sequence to a quantum permutation in full generality. To do so, we exploit some novel techniques introduced ... More
Examples of Connective C*-algebrasApr 15 2019We prove that any torsion free crystallographic group with the infinite abelianization is connective.
II$_1$ factors with exotic central sequence algebrasApr 15 2019We provide a class of separable II$_1$ factors $M$ whose central sequence algebra is not the "tail" algebra associated to any decreasing sequence of von Neumann subalgebras of $M$. This settles a question of McDuff \cite{Mc69d}.
Matrix Algebras with a Certain Compression Property IApr 15 2019An algebra $\mathcal{A}$ of $n\times n$ complex matrices is said to be projection compressible if $P\mathcal{A}P$ is an algebra for all orthogonal projections $P\in\mathbb{M}_n(\mathbb{C})$. Analogously, $\mathcal{A}$ is said to be idempotent compressible ... More
Matrix Algebras with a Certain Compression Property IApr 15 2019Apr 17 2019An algebra $\mathcal{A}$ of $n\times n$ complex matrices is said to be projection compressible if $P\mathcal{A}P$ is an algebra for all orthogonal projections $P\in\mathbb{M}_n(\mathbb{C})$. Analogously, $\mathcal{A}$ is said to be idempotent compressible ... More
Injectivity, crossed products, and amenable group actionsApr 14 2019This paper is motivated primarily by the question of when the maximal and reduced crossed products of a $G$-$C^*$-algebra agree (particularly inspired by results of Matsumura and Suzuki), and the relationships with various notions of amenability and injectivity. ... More
Prime II$_1$ factors arising from actions of product groupsApr 14 2019We prove that any II$_1$ factor arising from a free ergodic probability measure preserving action $\Gamma\curvearrowright X$ of a product $\Gamma=\Gamma_1\times\dots\times\Gamma_n$ of icc hyperbolic, free product or wreath product groups is prime, provided ... More
Subshifts, $λ$-graph bisystems and $C^*$-algebrasApr 13 2019We introduce a notion of $\lambda$-graph bisystem. It consists of a pair $({\frak L}^-, {\frak L}^+)$ of two labeled Bratteli diagrams ${\frak L}^-, {\frak L}^+$ over alphabets $\Sigma^-, \Sigma^+$, respectively, and satisfy certain compatibility condition ... More
Invariant subspaces of generalized Hardy algebras associated with compact abelian group actions on W*-algebrasApr 12 2019ABSTRACT. We consider an action of a compact group whose dual is archimedean linearly ordered or a direct product (or sum) of such groups on a von Neumann algebra, M. We define the generalized Hardy subspace of the Hilbert space of a standard representation ... More
Invariant subspaces of generalized Hardy algebras associated with compact abelian group actions on W*-algebrasApr 12 2019Apr 16 2019We consider an action of a compact group whose dual is archimedean linearly ordered or a direct product (or sum) of such groups on a von Neumann algebra, M. We define the generalized Hardy subspace of the Hilbert space of a standard representation the ... More
On orthogonal systems, two-sided bases and regular subfactorsApr 11 2019We prove that a regular subfator of type $II_1$ with finite Jones index always admits a two-sided Pimsner-Popa basis. This is preceeded by a pragmatic revisit of Popa's notion of orthogonal systems.
The groupoids of adaptable separated graphs and their type semigroupApr 10 2019Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup, which we prove is an $E^*$-unitary inverse semigroup. As ... More
Generating wandering subspaces for doubly commuting covariant representations of product systemsApr 10 2019We obtain Halmos-Richter type wandering subspace theorem for covariant representations over $C^*$-correspondences. We further explore the notion of Cauchy dual and obtain Shimorin type Wold decomposition for covariant representations over $C^*$-correspondences ... More
A K-theoretic Selberg trace formulaApr 09 2019Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of operators on the Hilbert space L^2(G/H) associated to compactly supported smooth functions ... More
Non-commutative Rényi Entropic Uncertainty PrinciplesApr 08 2019In this paper, we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters $0<p,q\leq \infty$. Furthermore, we establish R\'{e}nyi entropic uncertainty principles ... More
Refinement monoids and adaptable separated graphsApr 08 2019We define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated I-systems. ... More
Topological generation results for free unitary and orthogonal groupsApr 08 2019We show that for every $N\ge 3$ the free unitary group $U^+_N$ is topologically generated by its classical counterpart $U_N$ and the lower-rank $U^+_{N-1}$. This allows for a uniform inductive proof that a number of finiteness properties, known to hold ... More
A twisted local index formula for curved noncommutative two toriApr 08 2019We consider the Dirac operator of a general metric in the canonical conformal class on the noncommutative two torus, twisted by an idempotent (representing the $K$-theory class of a general noncommutative vector bundle), and derive a local formula for ... More
Strongly symmetric spectral convex bodies are Jordan algebra state spacesApr 07 2019We show that the strongly symmetric spectral convex compact sets are precisely the normalized state spaces of finite-dimensional simple Euclidean Jordan algebras and the simplices. Spectrality is the property that every state has a convex decomposition ... More
A revised augmented Cuntz semigroupApr 07 2019We revise the construction of the augmented Cuntz semigroup functor used by the first author to classify inductive limits of 1-dimensional noncommutative CW complexes. The original construction has good functorial properties when restricted to the class ... More
Geodesic neighborhoods in unitary orbits of self-adjoint operators of K+CApr 07 2019We study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U_(K+C) of the unitization of the compact operators K(H)+C, or equivalently, the quotient U_(K+C)/ U_Diag(K+C). We ... More
Tracial moment problems on hypercubesApr 07 2019In this paper we study the tracial moment problem on the hypercube $[-1,1]^n$. We propose the concept "sequential tracial $K$-moment problem" for sequences of scalar matrices and establish a sufficient condition for the solvability of the sequential tracial ... More
Tracial moment problems on hypercubesApr 07 2019Apr 09 2019In this paper we introduce the "tracial $K$-moment problem" and the "sequential matrix-valued $K$-moment problem" and show the equivalence of the solvability of these problems. Using a Haviland's theorem for matrix polynomials, we solve these $K$-moment ... More
Harmonic Models and BernoullicityApr 06 2019We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left orderable groups of large enough growth, as well as algebraic actions associated to certain lopsided elements in any left ... More
Roe bimodules as morphisms of discrete metric spacesApr 06 2019For two discrete metric spaces, $X$ and $Y$ we consider metrics on $X\sqcup Y$ compatible with the metrics on $X$ and $Y$. As morphisms from $X$ to $Y$ we consider the Roe bimodules, i.e. the norm closures of bounded finite propagation operators from ... More
Generalizing Lieb's Concavity Theorem via Operator InterpolationApr 05 2019We introduce the notion of $k$-trace and use interpolation of operators to prove the joint concavity of the function $(A,B)\mapsto\text{Tr}_k\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big]^\frac{1}{k}$, which generalizes Lieb's concavity ... More
(Non-)amenability of the Fourier algebra in the cb-multiplier normApr 05 2019For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{Mcb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that $A_{Mcb}(G)$ is not amenable if $G$ contains a ... More
(Non-)amenability of the Fourier algebra in the cb-multiplier normApr 05 2019Apr 18 2019For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{Mcb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that $A_{Mcb}(G)$ is not amenable if $G$ contains a ... More
A geometric approach to K-homology for Lie manifoldsApr 05 2019We prove that the computation of the Fredholm index for fully elliptic pseudodifferential operators on Lie manifolds can be reduced to the computation of the index of Dirac operators perturbed by smoothing operators. To this end we adapt to our framework ... More
Ozawa's class $\mathcal S$ for locally compact groups and unique prime factorizationApr 03 2019We study class $\mathcal S$ for locally compact groups. We characterize locally compact groups in this class as groups having an amenable action on a boundary that is small at infinity, generalizing a theorem of Ozawa. Using this characterization, we ... More
Homotopical and operator algebraic twisted K-theoryApr 03 2019Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the real ... More
Subdiagonal algebras with the Beurling type invariant subspacesApr 03 2019Let $\mathfrak A$ be a maximal subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$. If every right invariant subspace of $\mathfrak A$ in the non-commutative Hardy space $H^2$ is of Beurling type, then we say $\mathfrak A$ to be ... More
Two trace inequalities for operator functionsApr 02 2019In this paper we show that for a non-negative operator monotone function $f$ on $[0, \infty)$ such that $f(0)= 0$ and for any positive semidefinite matrices $A$ and $B$, $$ Tr((A-B)(f(A)-f(B))) \le Tr(|A-B|f(|A-B|)). $$ When the function $f$ is operator ... More
Dynamical sampling: mixed frame operators, representations and perturbationsApr 01 2019Motivated by recent progress in operator representation of frames, we investigate the frames of the form $ \{T^n \varphi\}_{n\in I}$ for $ I=\mathbb{N}, \mathbb{Z} $, and answer questions about representations, perturbations and frames induced by the ... More
Closed ideals and Lie ideals of $C_0(X) \otimes^{\min} A$Apr 01 2019In this article, we prove that a closed ideal of $C_0(X) \otimes^{\min} A$ is a finite sum of product ideals, where $X$ is a locally compact Hausdorff space and $A$ is $C^*$-algebra with only finitely many closed ideals. As an application, we characterize ... More
Inductive Limits for Systems of Toeplitz AlgebrasMar 30 2019This article deals with inductive systems of Toeplitz algebras over arbitrary directed sets. For such a system the family of its connecting injective $*$-homomorphisms is defined by a set of natural numbers satisfying a factorization property. The motivation ... More
A Note on Spectral Triples on the Quantum DiskMar 30 2019By modifying the ideas from our previous paper \cite{KMRSW}, we construct spectral triples from implementations of covariant derivations on the quantum disk.
Some applications of Scherer-Hol's theorem for polynomial matricesMar 30 2019In this paper we establish some applications of the Scherer-Hol's theorem for polynomial matrices. Firstly, we give a representation for polynomial matrices positive definite on subsets of compact polyhedra. Then we establish a Putinar-Vasilescu Positivstellensatz ... More
Quantum Semigroups from Synchronous GamesMar 29 2019We show that the C*-algebras associated with synchronous games give rise to certain quantum families of maps between the input and output sets of the game. In particular situations (e.g. for graph endomorphism games) these quantum families have a natural ... More
C*-algebras of a Cantor system with finitely many minimal subsets: structures, K-theories, and the index mapMar 28 2019We study homeomorphisms of a Cantor set with $k$ ($k < +\infty$) minimal invariant closed (but not open) subsets; we also study crossed product C*-algebras associated to these Cantor systems and their certain orbit-cut sub-C*-algebras. In the case that ... More
The graded structure of algebraic Cuntz-Pimsner ringsMar 28 2019The algebraic Cuntz-Pimsner rings are naturally $\mathbb{Z}$-graded rings that generalize both Leavitt path algebras and unperforated $\mathbb{Z}$-graded Steinberg algebras. We classify strongly, epsilon-strongly and nearly epsilon-strongly graded algebraic ... More
Partially isometric matrices: a brief and selective surveyMar 27 2019We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also discuss the unitary ... More
BMO-estimates for non-commutative vector valued Lipschitz functionsMar 26 2019We construct Markov semi-groups $\mathcal{T}$ and associated BMO-spaces on a finite von Neumann algebra $(\mathcal{M}, \tau)$ and obtain results for perturbations of commutators and non-commutative Lipschitz estimates. In particular, we prove that for ... More
Conditionally monotone independence and the associated products of graphsMar 26 2019We reduce the conditionally monotone (c-monotone) independence of Hasebe to tensor independence. For that purpose, we use the approach developed for the reduction of boolean, free and monotone independences to tensor independence. We apply the tensor ... More
Entangled edge states of corank one with positive partial transposesMar 26 2019We construct a parameterized family of $n\otimes n$ PPT states of corank one for each $n\ge 3$. With a suitable choice of parameters, we show that they are $n\otimes n$ PPT entangled edge states of corank one for $3\le n\le 800$. They violate the range ... More
Universal AF-algebrasMar 25 2019We study the approximately finite-dimensional (AF) $C^*$-algebras that appear as inductive limits of sequences of finite-dimensional $C^*$-algebras and left-invertible embeddings. We show that there is such a separable AF-algebra $\mathcal A_\mathfrak{F}$ ... More
Orthogonally additive polynomials on non-commutative $L^p$-spacesMar 25 2019Let $\mathcal{M}$ be a von Neumann algebra with a normal semifinite faithful trace $\tau$. We prove that every continuous $m$-homogeneous polynomial $P$ from $L^p(\mathcal{M},\tau)$, with $0<p<\infty$, into each topological linear space $X$ with the property ... More
Factorizable maps and traces on the universal free product of matrix algebrasMar 25 2019We relate factorizable quantum channels on $M_n$, for $n \ge 2$, via their Choi matrix, to certain correlation matrices, which, in turn, are shown to be parametrized by traces on the free unital product $M_n * M_n$. Factorizable maps that admit a finite ... More
Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers IMar 25 2019In this work, we solve the problem explicitly stated at the end of a paper of Junge, Mei and Parcet [JEMS2018]. More precisely, we prove that the Hodge-Dirac operator of the canonical "hidden" noncommutative geometry associated with a semigroup $(T_t)_{t ... More
Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers IMar 25 2019Apr 02 2019In this work, we solve the problem explicitly stated at the end of a paper of Junge, Mei and Parcet [JEMS2018]. More precisely, we prove that the Hodge-Dirac operator of the canonical "hidden" noncommutative geometry associated with a semigroup $(T_t)_{t ... More
Second Quantization and the Spectral ActionMar 22 2019We show that by incorporating chemical potentials one can extend the formalism of spectral action principle to Bosonic second quantization. In fact we show that the von Neumann entropy, the average energy, and the negative free energy of the state defined ... More
The Covariant Stone-von Neumann Theorem for Actions of Abelian Groups on $C^*$-algebras of Compact OperatorsMar 22 2019In this paper, we formulate and prove a version of the Stone-von Neumann Theorem for every $C^*$-dynamical system of the form $(G, \mathbb{K}(\mathcal{H}), \alpha)$, where $G$ is a locally compact Hausdorff abelian group and $\mathcal{H}$ is a Hilbert ... More
Grothendieck's inequalities for JB$^*$-triples: Proof of the Barton-Friedman conjectureMar 21 2019We prove that, given a constant $K> 2$ and a bounded linear operator $T$ from a JB$^*$-triple $E$ into a complex Hilbert space $H$, there exists a norm-one functional $\psi\in E^*$ satisfying $$\|T(x)\| \leq K \, \|T\| \, \|x\|_{\psi},$$ for all $x\in ... More
Grothendieck's inequalities for JB$^*$-triples: Proof of the Barton-Friedman conjectureMar 21 2019Mar 22 2019We prove that, given a constant $K> 2$ and a bounded linear operator $T$ from a JB$^*$-triple $E$ into a complex Hilbert space $H$, there exists a norm-one functional $\psi\in E^*$ satisfying $$\|T(x)\| \leq K \, \|T\| \, \|x\|_{\psi},$$ for all $x\in ... More
Limit operator theory for groupoidsMar 20 2019We extend the symbol calculus and study the limit operator theory for $\sigma$-compact, \'{e}tale and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact groups and discrete ... More
The atoms of the free additive convolution of two operator-valued distributionsMar 20 2019We find the atoms of the free additive convolution of two operator-valued distributions. This result allows one, via the linearization trick, to determine the atoms of the distribution of a selfadjoint polynomial in two free selfadjoint random variables. ... More
Maximal subgroups and von Neumann subalgebras with the Haagerup propertyMar 19 2019Apr 14 2019We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside $\mathbb{Z}^2 \rtimes SL_2(\mathbb{Z})$ and obtain several explicit instances where maximal Haagerup ... More
Maximal subgroups and von Neumann subalgebras with the Haagerup propertyMar 19 2019Mar 30 2019We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside $\mathbb{Z}^2 \rtimes SL_2(\mathbb{Z})$ and obtain several explicit instances where maximal Haagerup ... More
Maximal subgroups and von Neumann subalgebras with the Haagerup propertyMar 19 2019We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside $\mathbb{Z}^2 \rtimes SL_2(\mathbb{Z})$ and obtain several explicit instances where maximal Haagerup ... More
Wold decomposition for Doubly commuting isometric covariant representations of product systemsMar 19 2019We obtain a complete description of reducing subspaces, of a doubly commuting isometric covariant representation of a product system of $C^*$-correspondences, as a direct summand of Hilbert spaces. This result generalize and give a new proof of the Wold ... More
A Dolbeault-Dirac Spectral Triple for Quantum Projective SpaceMar 18 2019The notion of a K\"ahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantum flag manifolds. It was subsequently shown that any covariant positive ... More
The notion of observable and the moment problem for *-algebras and their GNS representationsMar 18 2019Dealing with $^*$-algebras $A$ (not $C^*$-algebras) the notion of observable is delicate. It is generally false that for $a=a^* \in A$ the operator $\pi_\omega(a)$ in a GNS rep. of a state $\omega$ is essentially selfadjoint: it is symmetric admitting ... More
Type classification of extremal quantized charactersMar 18 2019The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the representation associated ... More
An ultrapower construction of the multiplier algebra of a C*-algebraMar 18 2019Using ultrapowers of C*-algebras we provide a new construction of the multiplier algebra of a C*-algebra. This extends the work of Avsec and Goldbring in the article "Boundary amenability of groups via ultrapowers" to the setting of noncommutative and ... More
Orbit equivalence of higher-rank graphsMar 17 2019We study the notions of continuous orbit equivalence and eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs with finitely many vertices and no sinks or sources. We show that there ... More
Rigidity results for von Neumann algebras arising from mixing extensions of profinite actions of groups on probability spacesMar 17 2019Motivated by Popa's seminal work \cite{Po04}, in this paper, we provide a fairly large class of examples of group actions $\Gamma \curvearrowright X$ satisfying the extended Neshveyev-St\o rmer rigidity phenomenon \cite{NS03}: whenever $\Lambda \ca Y$ ... More
Fourier analysis for type III representations of the noncommutative torusMar 15 2019For the noncommutative 2-torus, we define and study Fourier transforms arising from representations of states with central supports in the bidual, exhibiting a possibly nontrivial modular structure (i.e. type III representations). We then prove the associated ... More
The C*-algebra of compact perturbations of diagonal operatorsMar 14 2019We study the elementary C*-algebra whose elements are the sum of a diagonal plus a compact operator. We describe the structure of the unitary group, the sets of ideals, automorhisms and projections.
On extension of quantum channels and operations to the space of relatively bounded operatorsMar 14 2019We analyse possibility to extend a quantum operation (sub-unital normal CP linear map on the algebra $B(H)$ of bounded operators on a separable Hilbert space $H$) to the space of all operators on $H$ relatively bounded w.r.t. a given positive unbounded ... More
Full factors and co-amenable inclusionsMar 13 2019We show that if $M$ is a full factor and $N \subset M$ is a co-amenable subfactor with expectation, then $N$ is also full. This answers a question of Popa from 1986. We also generalize a theorem of Tomatsu by showing that if $M$ is a full factor and $\sigma ... More
Quantization of Yang--Mills metrics on holomorphic vector bundlesMar 13 2019We investigate quantization properties of Hermitian metrics on holomorphic vector bundles over homogeneous compact K\"ahler manifolds. This allows us to study operators on Hilbert function spaces using vector bundles in a new way. We show that Yang--Mills ... More
A rigidity result for normalized subfactorsMar 12 2019We show a rigidity result for subfactors that are normalized by a representation of a lattice $\Gamma$ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of $L\Gamma$ which is normalized by the ... More
A rigidity result for normalized subfactorsMar 12 2019Apr 02 2019We show a rigidity result for subfactors that are normalized by a representation of a lattice $\Gamma$ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of $L\Gamma$ which is normalized by the ... More
The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebraMar 12 2019We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra $O_{n+1}$ for finite n in terms of K-theory. We show that there is an example of a space for which the homotopy set is a non-commutative group, ... More
Monoids, their boundaries, fractals and $C^\ast$-algebrasMar 12 2019In this note we establish some connections between the theory of self-similar fractals in the sense of John E. Hutchinson (cf. [3]) and the theory of boundary quotients of $C^\ast$-algebras associated to monoids. Although we must leave several important ... More
Compact quantum groups generated by their toriMar 09 2019Associated to any closed subgroup $G\subset U_N^+$ is a family of toral subgroups $T_Q\subset G$, indexed by the unitary matrices $Q\in U_N$. The family $\{T_Q|Q\in U_N\}$ is expected to encode the main properties of $G$, and there are several conjectures ... More
A note on the half-liberation operationMar 09 2019We propose a new approach to the half-liberation question, for the compact groups $T_N\subset G_N\subset U_N$, where $T_N=\mathbb Z_2^N$. Indeed, we can construct a quantum group $T_N^*\subset G_N^*\subset U_N^*$, simply by setting $G_N^*=<G_N,T_N^*>$. ... More
Projections over Quantum Homogeneous Odd-dimensional SpheresMar 07 2019We give a complete classification of isomorphism classes of finitely generated projective modules, or equivalently, unitary equivalence classes of projections, over the C*-algebra $C\left( \mathbb{S}_{q}^{2n+1}\right) $ of the quantum homogeneous sphere ... More
Tight and cover-to-join representations of semilattices and inverse semigroupsMar 07 2019We discuss the relationship between tight and cover-to-join representations of semilattices and inverse semigroups, showing that a slight extension of the former, together with an appropriate selection of co-domains, makes the two notions equivalent. ... More
The homotopy groups of the automorphism groups of Cuntz-Toeplitz algebrasMar 07 2019The Cuntz-Toeplitz algebra $E_{n+1}$ for $n\geq1$ is the universal C*-algebra generated by $n+1$ isometries with mutually orthogonal ranges. In this paper, we investigate the automorphism groups of the Cuntz-Toeplitz algebras and determine their homotopy ... More
The homotopy groups of the automorphism groups of Cuntz-Toeplitz algebrasMar 07 2019Mar 21 2019The Cuntz-Toeplitz algebra $E_{n+1}$ for $n\geq1$ is the universal C*-algebra generated by $n+1$ isometries with mutually orthogonal ranges. In this paper, we investigate the automorphism groups of the Cuntz-Toeplitz algebras and determine their homotopy ... More
Untwisting twisted spectral triplesMar 06 2019We examine the index data associated to twisted spectral triples and higher order spectral triples. In particular, we show that a Lipschitz regular twisted spectral triple can always be `logarithmically dampened' through functional calculus, to obtain ... More
Duplicable von Neumann AlgebrasMar 06 2019Recently, we have shown that von Neumann algebras form a model for Selinger and Valiron's quantum lambda calculus. In this paper, we explain our choice of interpretation of the duplicability operator "!" by studying those von Neumann algebras that might ... More
Right and left quotient of two bounded operators on Hilbert spacesMar 06 2019We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient ... More
Maps between rectangular matrix spaces preserving disjointness, (zero) triple product or normsMar 05 2019Let $M_{m,n}$ be the set of $m\times n$ real or complex rectangular matrices. Two matrices $A, B \in M_{m,n}$ are disjoint if $A^*B = 0_n$ and $AB^* = 0_m$. In this paper, characterization is given for linear maps $\Phi: M_{m,n} \rightarrow M_{r,s}$ sending ... More
Universal skein theory for group actionsMar 05 2019Given a group action on a finite set, we define the group-action model which consists of tensor network diagrams which are invariant under the group symmetry. In particular, group-action models can be realized as the even part of group-subgroup subfactor ... More
Weak frames in Hilbert C*-modules with application in Gabor analysisMar 05 2019In the first part of the paper we describe the dual \ell^2(A)^{\prime} of the standard Hilbert C*-module \ell^2(A) over an arbitrary (not necessarily unital) C*-algebra A. When A is a von Neumann algebra, this enables us to construct explicitly a self-dual ... More
CAT(0) cube complexes and inner amenabilityMar 05 2019Mar 11 2019We here consider inner amenability from a geometric and group theoretical perspective. We prove that for every non-elementary action of a group $G$ on a finite dimensional irreducible CAT(0) cube complex, there is a nonempty $G$-invariant closed convex ... More