Latest in math.oa

total 7820took 0.12s
Equivariant Callias index theory via coarse geometryFeb 20 2019The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over $C^*$-algebras of continuous ... More
Row contractions annihilated by interpolating vanishing idealsFeb 18 2019We study similarity classes of commuting row contractions annihilated by what we call higher order vanishing ideals of interpolating sequences. Our main result exhibits a Jordan-type direct sum decomposition for these row contractions. We illustrate how ... More
Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropyFeb 18 2019We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an algebraic action of $G$ on $X,$ there is a maximal, closed $G$-invariant subgroup $Y$ of $X$ so that the action of $G$ on $Y$ is weakly ... More
Sylvester matrix rank functions on crossed productsFeb 18 2019In this paper we consider the algebraic crossed product $\mathcal A := C_K(X) \rtimes_T \mathbb{Z}$ induced by a homeomorphism $T$ on the Cantor set $X$, where $K$ is an arbitrary field and $C_K(X)$ denotes the $K$-algebra of locally constant $K$-valued ... More
A C*-algebraic approach to interacting quantum field theoriesFeb 16 2019A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag-Kastler axioms, with insights gained in the perturbative approach to quantum ... More
A generalized type semigroup and dynamical comparisonFeb 16 2019In this paper, we construct a semigroup associated to an action of countable discrete group on a compact Hausdorff space, that can be regarded as a higher dimensional generalization of the type semigroup. Using this generalized type semigroup we obtain ... More
Normalizers and permutative endomorphisms of the $2$-adic ring $C^*$-algebraFeb 15 2019A complete description is provided for the unitary normalizer of the diagonal Cartan subalgebra $\mathcal{D}_2$ in the $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$, which generalizes and unifies analogous results for Cuntz and Bunce-Deddens algebras. Furthermore, ... More
Perturbation theory of KMS statesFeb 15 2019We extend the new perturbation formula of equilibrium states by Hastings to KMS states of general $W^*$-dynamical systems.
Spectral Action in Noncommutative GeometryFeb 14 2019What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry \`a la Connes, deliberately unveiling the answers to these questions. After a brief ... More
Interpolation between $L_0({\mathcal M},τ)$ and $L_\infty({\mathcal M},τ)$Feb 14 2019Let ${\mathcal M}$ be a semifinite von Neumann algebra with a faithful semifinite normal trace $\tau$. We show that the symmetrically $\Delta$-normed operator space $E({\mathcal M},\tau)$ corresponding to an arbitrary symmetrically $\Delta$-normed function ... More
Nest algebras in an arbitrary vector spaceFeb 12 2019We examine the properties of algebras of linear transformations that leave invariant all subspaces in a totally ordered lattice of subspaces of an arbitrary vector space. We compare our results with those that apply for the corresponding algebras of bounded ... More
Dynamical alternating groups, stability, property Gamma, and inner amenabilityFeb 11 2019We prove that the alternating group of a topologically free action of a countably infinite group $\Gamma$ on the Cantor set has the property that all of its $\ell^2$-Betti numbers vanish and, in the case that $\Gamma$ is amenable, is stable in the sense ... More
Analogues of Entropy in Bi-Free Probability Theory: MicrostatesFeb 11 2019In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are developed, such as ... More
Analogues of Entropy in Bi-Free Probability Theory: Non-MicrostateFeb 11 2019In this paper, we extend the notion of non-microstate free entropy to the bi-free setting. Using a diagrammatic approach involving bi-non-crossing diagrams, bi-free difference quotients are constructed as analogues of the free partial derivations. Adjoints ... More
Operator algebras of higher rank numerical semigroupsFeb 10 2019A higher rank numerical semigroup is a positive cone whose seminormalization is isomorphic to the free abelian semigroup. The corresponding nonselfadjoint semigroup algebras are known to provide examples that answer Arveson's Dilation Problem to the negative. ... More
Equivariant homologies for operator algebrasFeb 10 2019This is a survey of a variety of equivariant (co)homology theories for operator algebras. We briefly discuss a background on equivariant theories, such as equivariant $K$-theory and equivariant cyclic homology. As the main focus, we discuss a notion of ... More
Phase transitions on C*-algebras from actions of congruence monoids on rings of algebraic integersFeb 10 2019We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each $\beta\in[1,2]$, there is a unique KMS$_\beta$ state, and we prove that it ... More
Commuting maps on certain incidence algebrasFeb 09 2019Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, in this paper ... More
A tracially AF algebra which is not $\mathcal Z$-absorbingFeb 08 2019We show that there is a simple separable unital (non-nuclear) tracially AF algebra $A$ which does not absorb the Jiang-Su algebra $\mathcal Z$ tensorially, i.e. $A \ncong A\otimes\mathcal Z$.
Quantum Markov States on Cayley treesFeb 08 2019It is known that any locally faithful quantum Markov state (QMS) on one dimensional setting can be considered as a Gibbs state associated with Hamiltonian with commuting nearest-neighbor interactions. In our previous results, we have investigated quantum ... More
Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley treeFeb 08 2019The main aim of the present paper is to establish the existence of a phase transition for the quantum Ising model with competing XY interactions within the quantum Markov chain (QMC) scheme. In this scheme, we employ the $C^*$-algebraic approach to the ... More
Conditionally Free Reduced Products of Hilbert SpacesFeb 07 2019We present a product of pairs of pointed Hilbert spaces that, in the context of Boz\.ejko, Leinert and Speicher's theory of conditionally free probability, plays the role of the reduced free product of pointed Hilbert spaces, and thus gives a unified ... More
Laplacians on generalized smooth distributions as $C^*$-algebra multipliersFeb 07 2019In this paper, we discuss spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold. First, we give a survey of results on generalized smooth distributions on manifolds, Riemannian structures and associated ... More
$C^*$-algebras of right LCM monoids and their equilibrium statesFeb 07 2019We study the internal structure of $C^*$-algebras of right LCM monoids by means of isolating the core semigroup $C^*$-algebra as the coefficient algebra of a Fock-type module on which the full semigroup $C^*$-algebra admits a left action. If the semigroup ... More
The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relationsFeb 07 2019We prove that associated with each inverse semigroup $S$ is a Boolean inverse semigroup presented by what can be regarded as abstract Cuntz-Krieger relations; we call this the Exel completion of $S$. When the inverse semigroup has the additional property ... More
Subfactors and Hecke groupsFeb 07 2019We study a relation between the Hecke groups and the index of subfactors in a von Neumann algebra. Such a problem was raised by V. F. R. Jones. We solve the problem using the notion of a cluster C*-algebra.
A Hydrodynamic Exercise in Free Probability: Setting up Free Euler EquationsFeb 07 2019Feb 12 2019For the free probability analogue of Euclidean space endowed with the Gaussian measure we apply the approach of Arnold to derive Euler equations for a Lie algebra of non-commutative vector fields which preserve a certain trace. We extend the equations ... More
A Hydrodynamic Exercise in Free Probability: Setting up Free Euler EquationsFeb 07 2019For the free probability analogue of Euclidean space endowed with the Gaussian measure we apply the approach of Arnold to derive Euler equations for a Lie algebra of non-commutative vector fields which preserve a certain trace. We extend the equations ... More
Free Stein discrepancy as a regularity conditionFeb 06 2019We introduce a free probabilistic quantity called free Stein information, which is defined in terms of free Stein discrepancies. It turns out that this quantity exactly measures the von Neumann dimension of the closure of the domain of the adjoint of ... More
Finite dimensional semigroups of unitary endomorphisms of standard subspacesFeb 06 2019Let $M \subseteq B(H)$ be a von Neumann algebra with a cyclic separating unit vector $\Omega$ and the modular objects $(\Delta, J)$ obtained from the Tomita--Takesaki Theorem. Further, let $G \subseteq U(H)$ be a finite dimensional Lie group of unitary ... More
Unitary conjugacy for type III subfactors and W$^*$-superrigidityFeb 04 2019Let $A,B\subset M$ be inclusions of $\sigma$-finite von Neumann algebras such that $A$ and $B$ are images of faithful normal conditional expectations. In this article, we investigate Popa's intertwining condition $A\preceq_MB$ using their modular actions. ... More
On Bi-R-Diagonal Pairs of OperatorsFeb 04 2019We study the properties of the analogue of R-diagonal operators in the setting of bi-free probability. Products of bi-R-diagonal pairs of operators that are $*$-bi-free are studied and powers of such pairs are found to also be bi-R-diagonal. It is moreover ... More
A note on irreducible quadrilaterals of $II_1$ factorsFeb 01 2019Given any finite index quadrilateral $(N, P, Q, M)$ of $II_1$-factors, the notions of interior and exterior angles between $P$ and $Q$ were introduced in \cite{BDLR2017}. We determine the possible values of these angles when the quadrilateral is irreducible ... More
The product of lattice covolume and discrete series formal dimension: p-adic GL(2)Jan 31 2019Let $F$ be a nonarchimedean local field of characteristic $0$ and residue field of order not divisible by $2$. We show how to calculate the product of the covolume of a torsion-free lattice in $PGL(2,F)$ and the formal dimension of a discrete series representation ... More
Nuclear dimension of simple stably projectionless C*-algebrasJan 31 2019We prove that Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension at most 1. This completes the equivalence between finite nuclear dimension and Z-stability for simple, separable, nuclear, non-elementary C*-algebras.
Representations and the reduction theorem for ultragraph Leavitt path algebrasJan 31 2019In this paper we study representations of ultragraph Leavitt path algebras via branching systems and, using partial skew ring theory, prove the reduction theorem for these algebras. We apply the reduction theorem to show that ultragraph Leavitt path algebras ... More
On a presentation of the spin planar algebraJan 31 2019We define a certain abstract planar algebra by generators and relations, study various aspects of its structure, and then identify it with Jones' spin planar algebra.
Topological boundaries of unitary representationsJan 30 2019We introduce and study a generalization of the notion of the Furstenberg boundary of a discrete group $\Gamma$ to the setting of a general unitary representation $\pi: \Gamma \to B(\mathcal H_\pi)$. This space, which we call the "Furstenberg-Hamana boundary" ... More
Quantum double inclusions associated to a family of Kac algebra subfactorsJan 30 2019In \cite{Sde2018} we defined the notion of \textit{quantum double inclusion} associated to a finite-index and finite-depth subfactor and studied the quantum double inclusion associated to the Kac algebra subfactor $R^H \subset R$ where $H$ is a finite-dimensional ... More
A note on commutators in algebras of unbounded operatorsJan 30 2019We show that the identity is the sum of two commutators in the algebra of all operators affiliated with a von Neumann algebra of type II$_1$, settling a question, in the negative, that had puzzled a number of us.
Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebrasJan 29 2019Following a procedure due to V. Jones, using suitably normalized elements in a Temperley-Lieb-Jones (planar) algebra we introduce a 3-parametric family of unitary representations of the Thompson's group $F$ equipped with canonical (vacuum) vectors and ... More
The principal-symbol index map for an algebra of pseudodifferential operatorsJan 29 2019A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory index map associated ... More
Smale space C*-algebras have nonzero projectionsJan 29 2019The main result of the present paper is that the stable and unstable C*-algebras associated to a mixing Smale space always contain nonzero projections. This gives a positive answer to a question of the first listed author and Karen Strung and has implications ... More
Note on Wermuth's theorem on commuting operator exponentialsJan 29 2019We apply Wermuth's theorem on commuting operator exponentials to show that if $A, B \in B(X)$, $X$ being Banach space and $A$ of $2\pi i$-congruence free spectrum, then $e^A B = B e^A$ if and only if $AB=BA$. We employ this observation to provide alternative ... More
Existence and Uniqueness of the Karcher Mean on Unital $C^*$-algebrasJan 28 2019The Karcher mean on the cone $\Omega$ of invertible positive elements of the $C^*$-algebra $\mathcal{B}(E)$ of bounded operators on a Hilbert space $E$ has recently been extended to a contractive barycentric map on the space of $L^1$- probability measures ... More
Weak Cartan inclusions and non-Hausdorff groupoidsJan 28 2019Given a non necessarily Hausdorff, topologically free, twisted etale groupoid $(G ,L)$, we consider its "essential groupoid C*-algebra", denoted $C^*_{ess}(G, L)$, obtained by completing $C_c(G, L)$ with the smallest among all C*-seminorms coinciding ... More
$\mathrm{K}$-theory and homotopies of twists on ample groupoidsJan 27 2019This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism between the $\mathrm{K}$-theory ... More
When Nilpotence Implies Normality of Bounded Linear OperatorsJan 27 2019In this paper, we give conditions forcing nilpotent matrices (and bounded linear operators in general) to be null or equivalently to be normal. Therefore, a non-zero operator having e.g. a positive real part is never nilpotent. The case of quasinilpotence ... More
An Operad of Non-commutative Independences Defined by TreesJan 26 2019We study $N$-ary non-commutative notions of independence, which are given by trees and which generalize free, Boolean, and monotone independence. For every rooted subtree $\mathcal{T}$ of the $N$-regular tree, we define the $\mathcal{T}$-free product ... More
Local derivations on associative and Jordan matrix algebrasJan 25 2019In the present paper we prove that every additive (not necessarily homogenous) local inner derivation on the algebra of matrices over an arbitrary field is an inner derivation, and every local inner derivation on the ring of matrices over a finite ring ... More
Some Permanence for Large SubalgebraJan 25 2019In this paper, we give two properties of C*-algebra that could be deduced from the properties of its large subalgebra. Let A be an infinite dimensional simple unital C*-algebra and let B be a centrally large subalgebra of A, we prove that A has real rank ... More
Square functions for noncommutative differentially subordinate martingalesJan 25 2019We prove inequalities involving noncommutative differentially subordinate martingales. More precisely, we prove that if $x$ is a self-adjoint noncommutative martingale and $y$ is weakly differentially subordinate to $x$ then $y$ admits a decomposition ... More
The $C^*$-algebra of the Cartan motion groupsJan 24 2019Let $G_0=K\ltimes\p$ be the Cartan motion groups. Under some assumption on $G_0,$ we describe the $C^*$-algebra $C^*(G_0)$ of $G_0$ in terms of operator fields.
Pseudo-Polynomial Time Algorithm for Computing Moments of Polynomials in Free Semicircular ElementsJan 24 2019Jan 30 2019We consider about calculating $M$th moments of a given polynomial in free independent semicircular elements in free probability theory. By a naive approach, this calculation requires exponential time with respect to $M$. We explicitly give an algorithm ... More
Measures of weak non-compactness in preduals of von Neumann algebras and JBW$^*$-triplesJan 23 2019We prove, among other results, that three standard measures of weak non-compactness coincide in preduals of JBW$^*$-triples. This result is new even for preduals of von Neumann algebras. We further provide a characterization of JBW$^*$-triples with strongly ... More
Generating functionals for locally compact quantum groupsJan 22 2019Every symmetric generating functional of a convolution semigroup of states on a locally compact quantum group is shown to admit a dense unital $*$-subalgebra with core-like properties in its domain. On the other hand we prove that every normalised, symmetric, ... More
Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some modelsJan 22 2019We introduced in a previous paper a general notion of asymptotic morphism of a given local net of observables, which allows to describe the sectors of a corresponding scaling limit net. Here, as an application, we illustrate the general framework by analyzing ... More
A remark on the gauge action and noncommutative solitonsJan 21 2019We extend a result about the gauge action on noncommutative solitons by showing that a family of functions can be gauged away to a Gaussian using the quantification condition given in "On a gauge action on sigma model solitons" IDAQP(2018).
GCR and CCR Steinberg algebrasJan 18 2019Kaplansky introduced the notions of CCR and GCR $C^*$-algebras because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this paper we characterize when the algebra of an ample groupoid over ... More
Nuclear dimension of simple C*-algebrasJan 17 2019Feb 13 2019We compute the nuclear dimension of separable, simple, unital, nuclear, Z-stable C*-algebras. This makes classification accessible from Z-stability and in particular brings large classes of C*-algebras associated to free and minimal actions of amenable ... More
Nuclear dimension of simple C*-algebrasJan 17 2019We compute the nuclear dimension of separable, simple, unital, nuclear and Z-stable C*-algebras. This makes classification of simple, unital, nuclear C*-algebras accessible from Z-stability and so brings large classes of C*-algebras associated to free ... More
Lie Triple Derivations of Incidence AlgebrasJan 17 2019Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, we prove in this ... More
The approximation property and exactness of locally compact groupsJan 16 2019We extend a theorem of Haagerup and Kraus in the C*-algebra context: for a locally compact group with the approximation property (AP), the reduced C*-crossed product construction preserves the strong operator approximation property (SOAP). In particular ... More
On the ellipticity of operators associated with Morse-Smale diffeomorphismsJan 15 2019We consider the operator algebra generated by pseudodifferential operators on a closed smooth surface and shift operator induced by a Morse--Smale diffeomorphism of this surface. Elements in this algebra are considered as operators in the scale of Sobolev ... More
Universal Continuous Calculus for Su*-AlgebrasJan 13 2019Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and uniformly complete), ... More
C*-algebras from actions of congruence monoids on rings of algebraic integersJan 13 2019Let $K$ be a number field with ring of integers $R$. Given a modulus $\mathfrak{m}$ for $K$ and a group $\Gamma$ of residues modulo $\mathfrak{m}$, we consider the semi-direct product $R\rtimes R_{\mathfrak{m},\Gamma}$ obtained by restricting the multiplicative ... More
Some generalizations of K-g-frames in Hilbert $C^{\ast}$- moduleJan 11 2019In this papers we investigate the g-frame and Bessel g-sequence related to a linear bounded operator $K$ in Hilbert $C^{\ast}$-module and we establish some results.
The duals of $\ast$-operator frames for $End_{\mathcal{A}}^{\ast}(H)$Jan 11 2019Frames play significant role in signal and image processing, which leads to many applications in differents fields. In this paper we define the dual of $\ast$-operator frames and we show their propreties obtained in Hilbert $\mathcal{A}$-modules and we ... More
On vector-valued characters for noncommutative function algebrasJan 08 2019Let A be a closed subalgebra of a C*-algebra, that is a closed algebra of Hilbert space operators. We generalize to such operator algebras $A$ several key theorems and concepts from the theory of classical function algebras. In particular we consider ... More
Entropy of Coherent ExcitationsJan 08 2019We provide a rigorous, explicit formula for the vacuum relative entropy of a coherent state on wedge local von Neumann algebras associated with a free, neutral quantum field theory on the Minkowski spacetime of arbitrary spacetime dimension. The second ... More
Delocalized eta invariants, cyclic cohomology and higher rho invariantsJan 07 2019The first main result of this article is to prove the convergence of Lott's delocalized eta invariant holds for all invertible operators. Our second main result is to construct a pairing between delocalized cyclic cocycles of the group algebra of the ... More
Invariant Markov semigroups on quantum homogeneous spacesJan 03 2019Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between such invariant ... More
Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learningDec 31 2018Jan 29 2019The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent homology and the theory of group actions. We define group-equivariant non-expansive ... More
Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformationsDec 30 2018We consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an elliptic operator. ... More
Bigalois extensions and the graph isomorphism gameDec 30 2018We study the graph isomorphism game that arises in quantum information theory from the perspective of bigalois extensions of compact quantum groups. We show that every algebraic quantum isomorphism between a pair of (quantum) graphs $X$ and $Y$ arises ... More
$R$-diagonal and $η$-diagonal Pairs of Random VariablesDec 29 2018This paper is devoted to studying $R$-diagonal and $\eta$-diagonal pairs of random variables. We prove that the product pair of two bi-free pairs of random variables is $R$-diagonal, if at least one of the two pairs is $R$-diagonal. Calculating formulae ... More
Identifiability of parametric random matrix modelsDec 27 2018We investigate parameter identifiability of spectral distributions of random matrices. In particular, we treat compound Wishart type and signal-plus-noise type. We show that each model is identifiable up to some kind of rotation of parameter space. Our ... More
Jordan operator algebras revisitedDec 24 2018Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative ... More
When is Every Quasi-Multiplier a Multiplier?Dec 24 2018We answer the title question for sigma-unital C*-algebras. The answer is that the algebra must be the direct sum of a dual C*-algebra and a C*-algebra satisfying a certain local unitality condition. We also discuss similar problems in the context of Hilbert ... More
Rigidity theory for $C^*$-dynamical systems and the "Pedersen Rigidity Problem", IIDec 24 2018This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen's theorem, which does ... More
Failure of the trilinear operator space Grothendieck theoremDec 23 2018Jan 16 2019We give a counterexample to a trilinear version of the operator space Grothendieck theorem. In particular, we show that for trilinear forms on $\ell_\infty$, the ratio of the symmetrized completely bounded norm and the jointly completely bounded norm ... More
Hyperrigid generators in C*-algebrasDec 20 2018In this article, we show that, if $S\in \mathcal{B}(H)$ is irreducible and essential unitary, then $\{S,SS^*\}$ is a hyperrigid generator for the unital $C^*$-algebra $\mathcal{T}$ generated by $\{S,SS^*\}$. We prove that, if $T$ is an operator in $\mathcal{B}(H)$ ... More
On $q$-tensor product of Cuntz algebrasDec 20 2018Jan 28 2019We consider $C^*$-algebra $\mathcal{E}_{n,m}^q$, which is a $q$-twist of two Cuntz-Toeplitz algebras. For the case $|q|<1$ we give an explicit formula, which untwists the $q$-deformation, thus showing that the isomorphism class of $\mathcal{E}_{n,m}^q$ ... More
Structure of extensions of free Araki-Woods factorsDec 20 2018We investigate the structure of crossed product von Neumann algebras arising from Bogoljubov actions of countable groups on Shlyakhtenko's free Araki-Woods factors. Among other results, we settle the questions of factoriality and Connes' type classification. ... More
Unitary invariants for commuting tuples of hypercontractionsDec 19 2018In this paper, we introduce the notion of characteristic functions for commuting tuples of $m$-hypercontractions on Hilbert spaces and investigate some properties. We prove that the characteristic function is a complete unitary invariant. We also offer ... More
Roots of Completely Positive MapsDec 19 2018We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots and as continuous one-parameter semigroups of roots. We present several general ... More
Matrix algebras over algebras of unbounded operatorsDec 17 2018Let $\mathscr{M}$ be a $II_1$ factor acting on the Hilbert space $\mathscr{H}$, and $\mathscr{M}_{\textrm{aff}}$ be the Murray-von Neumann algebra of closed densely-defined operators affiliated with $\mathscr{M}$. Let $\tau$ ($\tau_n$, respectively) denote ... More
On C*-completions of discrete quantum group ringsDec 15 2018We discuss just infiniteness of C*-algebras associated to discrete quantum groups and relate it to the C*-uniqueness of the quantum groups in question, i.e. to the uniqueness of a C*-completion of the underlying Hopf *-algebra. It is shown that duals ... More
From a Kac algebra subfactor to Drinfeld doubleDec 12 2018Given a finite-index and finite-depth subfactor, we define the notion of \textit{quantum double inclusion} - a certain unital inclusion of von Neumann algebras constructed from the given subfactor - which is closely related to that of Ocneanu's asymptotic ... More
Spectral Theory in a Twisted Groupoid Setting: Spectral Decompositions, Localization and FredholmnessDec 11 2018We study bounded operators defined in terms of the regular representations of the $C^*$-algebra of an amenable, Hausdorff, second countable locally compact groupoid endowed with a continuous $2$-cocycle. We concentrate on spectral quantities associated ... More
Decidability of flow equivalence and isomorphism problems for graph C*-algebras and quiver representationsDec 11 2018We note that the deep results of Grunewald and Segal on algorithmic problems for arithmetic groups imply the decidability of several matrix equivalence problems involving poset-blocked matrices over Z. Consequently, results of Eilers, Restorff, Ruiz and ... More
On stable maps of operator algebrasDec 11 2018We define a strong Morita-type equivalence $\sim _{\sigma \Delta }$ for operator algebras. We prove that $A\sim _{\sigma \Delta }B$ if and only if $A$ and $B$ are stably isomorphic. We also define a relation $\subset _{\sigma \Delta }$ for operator algebras. ... More
Variational principles for spectral radius of weighted endomorphisms of $C(X,D)$Dec 11 2018We give formulas for the spectral radius of weighted endomorphisms $a\alpha: C(X,D)\to C(X,D)$, $a\in C(X,D)$, where $X$ is a compact Hausdorff space and $D$ is a unital Banach algebra. Under the assumption that $\alpha(C(X)\otimes 1)\subseteq \alpha(1)C(X)\otimes ... More
Some aspects of number theory related to phase operatorsDec 09 2018Dec 22 2018We first extend the multiplicativity property of arithmetic functions to the setting of operators on the Fock space. Secondly, we use phase operators to get representation of some extended arithmetic functions by operators on the Hardy space. Finally, ... More
Essential Normality - a Unified Approach in Terms of Local DecompositionsDec 07 2018In this paper, we define the asymptotic stable division property for submodules of the Bergman module. We show that under a mild condition, a submodule with the asymptotic stable division property is p-essentially normal for all p>n. A new technique is ... More
On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type III$_1$Dec 07 2018We show the relative bicentralizer flow and the relative flow of weights are isomorphic for an inclusion of injective factors of type III$_1$ with finite index, or an irreducible discrete inclusion whose small algebra is an injective factor of type III$_1$. ... More
Asymptotic free independence and entry permutations for Gaussian random matricesDec 04 2018The paper presents conditions on entry permutations that induce asymptotic freeness when acting on Gaussian random matrices. The class of permutations described includes the matrix transpose, as well as entry permutations relevant in Quantum Information ... More
On the structure of the set of positive mapsDec 04 2018The structure of the set of positive maps $T: \qA \to \cB(\cH)$ ($\qA$ a $C^*$-algebra) is described. In particular, the origin of non-decomposable maps is clarified.
Tensor-product coaction functorsDec 03 2018For a discrete group $G$, we develop a `$G$-balanced tensor product' of two coactions $(A,\delta)$ and $(B,\epsilon)$, which takes place on a certain subalgebra of the maximal tensor product $A\otimes_{\max} B$. Our motivation for this is that we are ... More
Admissible vectors, convolution Hilbert algebras, idempotents and weightsNov 30 2018Admissible vectors for unitary representations of locally compact groups are the basis for group-frame and coherent state expansions. This work studies the existence and characterization of admissible vectors. Convolution Hilbert algebras, positive functions, ... More