Latest in math.oa

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The cb-norm approximation of generalized skew derivations by elementary operatorsJun 13 2019Let $A$ be a ring and $\sigma: A \to A$ a ring endomorphism. A generalized skew (or $\sigma$-)derivation of $A$ is an additive map $d: A \to A$ for which there exists a map $\delta:A \to A$ such that $d(xy)=\delta(x)y+\sigma(x)d(y)$ for all $x,y \in A$. ... More
Polish groups of unitariesJun 13 2019We study the question of which Polish groups which can be realized as subgroups of the unitary group of a separable infinite-dimensional Hilbert space. We also show that the unitary group of a separable unital C$^*$-algebra with finite exponential length ... More
Haagerup property for wreath products constructed with Thompson's groupsJun 10 2019Using recent techniques introduced by Jones we prove that a large family of discrete groups and groupoids have the Haagerup property. In particular, we show that if G is a discrete group with the Haagerup property, then the wreath product $\oplus_{Q_2}G\rtimes ... More
Semi-Fredholm Theory on Hilbert C*-modulesJun 07 2019In this paper we establish the semi-Fredholm theory on Hilbert C*-modules as a continuation of Fredholm theory on Hilbert C*-modules established by Mishchenko and Fomenko. We give a definition of a semi-Fredholm operator on Hilbert C*-module and prove ... More
Groupoid algebras as covariance algebrasJun 07 2019Suppose $\mathcal{G}$ is a second-countable locally compact Hausdorff \'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\mathcal{G}\rightarrow G$ is a continuous cocycle. We derive conditions on the cocycle such ... More
The Plancherel formula for complex semisimple quantum groupsJun 06 2019We calculate the Plancherel formula for complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups. As a consequence we obtain a concrete description of their associated reduced group $ C^* $-algebras. ... More
Morita Equivalence of W*-Correspondences and their Hardy AlgebrasJun 06 2019Muhly and Solel developed a notion of Morita equivalence for $C^{*}$- correspondences, which they used to show that if two $C^{*}$-correspondences $E$ and $F$ are Morita equivalent then their tensor algebras $\mathcal{T}_{+}(E)$ and $\mathcal{T}_{+}(F)$ ... More
The nuclear dimension of $\mathcal O_\infty$-stable $C^*$-algebrasJun 05 2019We show that every nuclear $\mathcal O_\infty$-stable *-homomorphism with a separable exact domain has nuclear dimension at most 1. In particular separable, nuclear, $\mathcal O_\infty$-stable C*-algebras have nuclear dimension 1. We also characterise ... More
Quantization of subgroups of the affine groupJun 05 2019Consider a locally compact group $G=Q\ltimes V$ such that $V$ is abelian and the action of $Q$ on the dual abelian group $\hat V$ has a free orbit of full measure. We show that such a group $G$ can be quantized in three equivalent ways: (1) by reflecting ... More
$C^*$-algebras associated with two-sided subshiftsJun 05 2019This paper is a continuation of the paper entitled "Subshifts, $\lambda$-graph bisystems and $C^*$-algebras", arXiv:1904.06464. A $\lambda$-graph bisystem consists of a pair of two labeled Bratteli diagrams satisfying certain compatibility condition on ... More
Automorphism-invariant positive definite functions on free groupsJun 04 2019In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new perspectives and ... More
Connective Bieberbach groupsJun 03 2019We prove that a Bieberbach group with trivial center is not connective and use this property to show that a Bieberbach group is connective if and only if it is poly-Z.
A Beurling-Blecher-Labuschagne theorem for Haagerup noncommutative $L^p$ spacesJun 03 2019Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be maximal subdiagonal subalgebra of $\mathcal{M}$. We prove a Beurling-Blecher-Labuschagne theorem for $\mathcal{A}$-invariant ... More
Remarks on a free analogue of the beta prime distributionJun 03 2019We introduce the free analogue of the classical beta prime distribution by the multiplicative free convolution of the free Poisson and the reciprocal of free Poisson distributions, and related free analogues of the classical $F$, $T$, and beta distributions. ... More
Tilings, traces and trianglesJun 02 2019This paper deals with random substitutions on a finite set of prototiles. The assumptions on the types of substitution rules allowed are very weak, leading to very general constructions. Using renormalization tools applied to elements from operator algebras ... More
Tilings, traces and trianglesJun 02 2019Jun 07 2019This paper deals with random substitutions on a finite set of prototiles. The assumptions on the types of substitution rules allowed are very weak, leading to very general constructions. Using renormalization tools applied to elements from operator algebras ... More
On K-theoretic invariants of semigroup C*-algebras from actions of congruence monoidsJun 02 2019We study semigroup C*-algebras of semigroups associated with number fields and initial data arising naturally from class field theory. Using K-theoretic invariants, we investigate how much information about the initial number-theoretic data is encoded ... More
The Scott rank of Polish metric spacesJun 02 2019We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational $q > 0$, there is a relation $R_{<q}(x,y)$ stating that the distance of $x$ and $y $ is less than $q$. ... More
On $k$ point density problem for band-diagonal $M$-basesJun 01 2019In the early 1990s the works of Larson, Wogen and Argyros, Lambrou, Longstaff disclosed an example of a strong tridiagonal $M$-basis that was not rank one dense. Later Katavolos, Lambrou and Papadakis studied $k$ point density property of this example. ... More
Notes on derivations of Murray--von Neumann algebrasJun 01 2019Let $\mathcal{M}$ be a type II$_1$ von Neumann factor and let $S(\mathcal{M})$ be the associated Murray-von Neumann algebra of all measurable operators affiliated to $\mathcal{M}.$ We extend a result of Kadison and Liu \cite{KL} by showing that any derivation ... More
K-stability of continuous C(X)-algebrasMay 31 2019A C*-algebra is said to be K-stable if its nonstable K-groups are naturally isomorphic to the usual K-theory groups. We study continuous $C(X)$-algebras, each of whose fibers are K-stable. We show that such an algebra is itself K-stable under the assumption ... More
Generality of Lieb's Concavity TheoremMay 30 2019We show that Lieb's concavity theorem holds more generally for any unitarily invariant matrix function $\phi:\mathbf{H}^n_+\rightarrow \mathbb{R}$ that is monotone and concave. Concretely, we prove the joint concavity of the function $(A,B) \mapsto\phi\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big] ... More
On pathological properties of fixed point algebras in Kirchberg algebrasMay 30 2019We investigate how the fixed point algebra of a C*-dynamical system can differ from the underlying C*-algebra. For any exact group $\Gamma$ and any infinite group $\Lambda$, we construct an outer action of $\Lambda$ on the Cuntz algebra $\mathcal{O}_2$ ... More
The SYK Model and the q-Brownian MotionMay 30 2019We extend recent results on the asymptotic eigenvalue distribution of the SYK model to the multivariate case and relate those limits with the q-Brownian motion, a non-commutative deformation of classical Brownian motion.
On partial skew groupoids ringsMay 29 2019Given a partial action $\alpha$ of a connected groupoid $\mathcal{G}$ on an associative ring $A$ we investigate under what conditions the partial skew groupoid ring $A\star_{\alpha}\mathcal{G}$ can be realized as a partial skew group ring. In such a case ... More
Higher invariants in noncommutative geometryMay 29 2019We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
A Lichnerowicz Vanishing Theorem for the Maximal Roe AlgebraMay 29 2019We show that if a discrete group acts properly and isometrically on a spin manifold of bounded geometry with a uniformly positive scalar curvature metric, then the maximal equivariant index of the Dirac operator vanishes in K-theory of the maximal equivariant ... More
A note on crossed products of rotation algebrasMay 29 2019We compute the $K$-theory of crossed products of rotation algebras $\mathcal{A}_\theta$, for any real angle $\theta$, by matrices in $\mathrm{SL}(2,\mathbb{Z})$ with infinite order. Using techniques of continuous fields, we show that the canonical inclusion ... More
Berger-Coburn theorem, localized operators, and the Toeplitz algebraMay 29 2019We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz operators and extend this theorem to the setting of $p$-Fock spaces $(1\leq p \leq \infty)$. We present an overview of recent results by various authors on the compactness ... More
Concrete Barriers to Quantifier Elimination in Finite-Dimensional C*-algebrasMay 29 2019Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*-algebras that admit quantifier elimination in continuous logic are $\mathbb{C},$ $\mathbb{C}^2,$ $M_2(\mathbb{C}),$ and the continuous functions on the Cantor set. ... More
Concrete Barriers to Quantifier Elimination in Finite-Dimensional C*-algebrasMay 29 2019May 30 2019Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*-algebras that admit quantifier elimination in continuous logic are $\mathbb{C},$ $\mathbb{C}^2,$ $M_2(\mathbb{C}),$ and the continuous functions on the Cantor set. ... More
Hausdorffifized algebraic $K_1$ group and invariants for $C^*$-algebras with the ideal propertyMay 28 2019A $C^*$-algebra $A$ is said to have the ideal property if each closed two-sided ideal of $A$ is generated by the projections inside the ideal, as a closed two sided ideal. $C^*$-algebras with the ideal property are generalization and unification of real ... More
On the inductive limit of direct sums of simple TAI algebrasMay 28 2019An ATAI (or ATAF, respectively) algebra, introduced in [Jiang1] (or in [Fa] respectively) is an inductive limit $\lim\limits_{n\rightarrow\infty}(A_{n}=\bigoplus\limits_{i=1}A_{n}^{i},\phi_{nm})$, where each $A_{n}^{i}$ is a simple separable nuclear TAI ... More
On the Decomposition Theorems for C*-algebrasMay 28 2019Elliott dimension drop interval algebra is an important class among all $C^*$-algebras in the classification theory. Especially, they are building stones of $\mathcal{AHD}$ algebra and the latter contains all $AH$ algebras with the ideal property of no ... More
Kawada-Itô-Kelley Theorem for Quantum SemigroupsMay 28 2019Idempotent states on locally compact quantum semigroups with weak cancellation properties are shown to be Haar states on a certain sub-object described by an operator system with comultiplication. We also give a characterization of the situation when ... More
$L_2$-cohomology, derivations and quantum Markov semi-groups on $q$-Gaussian algebrasMay 28 2019We study (quasi-)cohomological properties through an analysis of quantum Markov semi-groups. We construct higher order Hochschild cocycles using gradient forms associated with a quantum Markov semi-group. By using Schatten-$\mathcal{S}_p$ estimates we ... More
On $\mathbb{Z}_2$-indices for ground states of fermionic chainsMay 28 2019For parity-conserving fermionic chains, we review how to associate $\mathbb{Z}_2$-indices to ground states in finite systems with quadratic and higher-order interactions as well as to quasifree ground states on the infinite CAR algebra. It is shown that ... More
The Novikov ConjectureMay 27 2019We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
Ground states for generalized gauge actions on UHF algebrasMay 27 2019We describe the structure of ground states and ceiling states for generalized gauge actions on an UHF algebra. It is shown that both sets are affinely homeomorphic to the state space of a unital AF algebra, and that any pair of unital AF algebras can ... More
Realizations of non-commutative rational functions around a matrix centre, I: synthesis, minimal realizations and evaluation on stably finite algebrasMay 27 2019In this paper we generalize classical results regarding minimal realizations of non-commutative (nc) rational functions using nc Fornasini-Marchesini realizations which are centred at an arbitrary matrix point. We prove the existence and uniqueness of ... More
A Note Around Operator Bellman InequalityMay 25 2019In this paper, we shall give an extension of operator Bellman inequality. This result is estimated via Kantorovich constant.
Hyperrigidity of C*-correspondencesMay 24 2019We show that hyperrigidity for a C*-correspondence $(A,X)$ is equivalent to non-degeneracy of the left action of the Katsura ideal $\mathcal{J}_X$ on $X$. Due to the work of Katsoulis and Ramsey, our result shows that if $G$ is a locally compact group ... More
The hyperrigidity of tensor algebras of C$^*$-correspondencesMay 24 2019Given a C$^*$-correspondence $X$, we give necessary and sufficient conditions for the tensor algebra $\mathcal T_X^+$ to be hyperrigid. In the case where $X$ is coming from a topological graph we obtain a complete characterization.
The hyperrigidity of tensor algebras of C$^*$-correspondencesMay 24 2019May 27 2019Given a C$^*$-correspondence $X$, we give necessary and sufficient conditions for the tensor algebra $\mathcal T_X^+$ to be hyperrigid. In the case where $X$ is coming from a topological graph we obtain a complete characterization.
The Baum-Connes conjecture: an extended surveyMay 24 2019We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
Equivalence bundles over a finite group and strong Morita equivalence for unital inclusions of unital $C^*$-algebrasMay 24 2019Let $\mathcal{A}= \{A_t \}_{t \in G}$ and $\mathcal{B}= \{B_t \}_{t\in G}$ be $C^*$-algebraic bundles over a finite group $G$. Let $C=\oplus_{t \in G}A_t$ and $D=\oplus_{t\in G}B_t$. Also, let $A=A_e$ and $B=B_e$, where $e$ is the unit element in $G$. ... More
Tensor product decompositions and rigidity of full factorsMay 24 2019We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We use this to show ... More
Rohlin actions of finite groups on the Razak-Jacelon algebraMay 23 2019Let $A$ be a simple separable nuclear C$^*$-algebra with a unique tracial state and no unbounded traces, and let $\alpha$ be a strongly outer action of a finite group $G$ on $A$. In this paper, we show that $\alpha\otimes \mathrm{id}$ on $A\otimes\mathcal{W}$ ... More
Laplace-Beltrami Operators on Noncommutative ToriMay 22 2019In this paper, we construct Laplace-Beltrami operators associated with arbitrary Riemannian metrics on noncommutative tori of any dimension. These operators enjoy the main properties of the Laplace-Beltrami operators on ordinary Riemannian manifolds. ... More
Interpolation of quasi noncommutative $L_p$-spacesMay 21 2019Let $\mathcal{M}$ be a ($\sigma$-finite) von Neumann algebra associated with a normal faithful state $\phi.$ We prove a complex interpolation result for a couple of two (quasi) Haagerup noncommutative $L_p$-spaces $L_{p_0} (\mathcal{M}, \phi)$ and $L_{p_1} ... More
Noncommutative Choquet theoryMay 21 2019We introduce a new and extensive theory of noncommutative convexity along with a corresponding theory of noncommutative functions. We establish noncommutative analogues of the fundamental results from classical convexity theory, and apply these ideas ... More
The free field: realization via unbounded operators and Atiyah propertyMay 20 2019Let $X_1,\dots,X_n$ be operators in a finite von Neumann algebra and consider their division closure in the affiliated unbounded operators. We address the question when this division closure is a skew field (aka division ring) and when it is the free ... More
Groupoids: Substructures and homomorphismsMay 20 2019Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids and normal ... More
Matrix liberation process II: Relation to orbital free entropyMay 20 2019We investigate the concept of orbital free entropy from the viewpoint of matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation principle for ... More
Strong Novikov conjecture for low degree cohomology and exotic group C*-algebrasMay 19 2019We strengthen a result of Hanke-Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group C*-algebra even holds for the reduced group C*-algebra. To achieve this we provide a ... More
Orbit equivalence rigidity for product actionsMay 18 2019Let $\Gamma_1,\dots,\Gamma_n$ be hyperbolic, property (T) groups, for some $n\ge 1$. We prove that if a product $\Gamma_1\times\dots\times\Gamma_n \curvearrowright X_1\times\dots\times X_n$ of measure preserving actions is stably orbit equivalent to a ... More
Non-Linear New Product $A^*B-B^*A$ Derivations on $\ast$-AlgebrasMay 18 2019Let $\mathcal{A}$ be a prime $\ast$-algebra. In this paper, we suppose that $\Phi:\mathcal{A}\to\mathcal{A}$ satisfies $$\Phi(A\diamond B)=\Phi(A)\diamond B+A\diamond\Phi(B)$$ where $A\diamond B = A^{*}B - B^{*}A$ for all $A,B\in\mathcal{A}$ .We will ... More
Unbounded Derivations in Algebras Associated with Monothetic GroupsMay 17 2019Given an infinite, compact, monothetic group $G$ we study decompositions and structure of unbounded derivations in a crossed product C$^*$-algebra $C(G)\rtimes\Z$ obtained from a translation on $G$ by a generator of a dense cyclic subgroup. We also study ... More
The Balian-Low theorem for locally compact abelian groups and vector bundlesMay 16 2019Let $\Lambda$ be a lattice in a second countable, locally compact abelian group $G$ with annihilator $\Lambda^{\perp} \subseteq \widehat{G}$. We investigate the validity of the following statement: For every $\eta$ in the Feichtinger algebra $S_0(G)$, ... More
The Modular Symmetry of Markov MapsMay 16 2019A state-preserving automorphism of a von Neumann algebra induces a canonical unitary operator on the GNS Hilbert space of the state which fixes the vacuum. This unitary commutes with both the modular operator of the state and its modular conjugation. ... More
Noncommutative Joinings IIMay 16 2019This paper is a continuation of the authors' previous work on noncommutative joinings, and contains a study of relative independence of W$^*$-dynamical systems. We prove that, given any separable locally compact group $G$, an ergodic W$^{*}$-dynamical ... More
On Noncommutative JoiningsMay 16 2019This paper extends the classical theory of joinings of measurable dynamical systems to the noncommutative setting from several interconnected points of view. Among these is a particularly fruitful identification of joinings with equivariant quantum channels ... More
Embedding Semigroup $C^*$-algebras into Inductive LimitsMay 16 2019The note is concerned with inductive systems of Toeplitz algebras and their $*$-homomorphisms over arbitrary partially ordered sets. The Toeplitz algebra is the reduced semigroup $C^*$-algebra for the additive semigroup of non-negative integers. It is ... More
Geometry of the set of synchronous quantum correlationsMay 15 2019We provide a complete geometric description of the set of synchronous quantum correlations for the three experiment two outcome scenario. We show that these correlations form a closed set. Moreover, every correlation in this set can be realized using ... More
Contractive projections and real positive maps on operator algebrasMay 14 2019Our main goal here is to study contractive projections on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and JB algebras due to Choi, Effros, ... More
Contractive projections and real positive maps on operator algebrasMay 14 2019May 29 2019Our main goal here is to study contractive projections on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and JB algebras due to Choi, Effros, ... More
On spectral measures for certain unitary representations of R. Thompson's group FMay 14 2019The Hilbert space $\mathcal H$ of backward renormalisation of an anyonic quantum spin chain affords a unitary representation of Thompson's group $F$ via local scale transformations. Given a vector in the canonical dense subspace of $\mathcal H$ we show ... More
The Hadamard product in a crossed product C*-algebraMay 14 2019We show that for a C*-algebra A and a discrete group G with an action of G on A, the reduced crossed product C*-algebra possesses a natural generalization of the convolution product, which we suggest should be named the Hadamard product. We show that ... More
On quantum Strassen's theoremMay 14 2019Strassen's theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite Strassen's theorem is reduced ... More
A von Neumann algebraic approach to self-similar group actionsMay 10 2019We study some relations between self-similar group actions and operator algebras. We consider KMS states on the Cuntz--Pimsner algebras constructed by Nekrashevych from self-similar actions and the GNS representations of the KMS states. The KMS states ... More
A von Neumann algebraic approach to self-similar group actionsMay 10 2019May 20 2019We study some relations between self-similar group actions and operator algebras. We consider KMS states on the Cuntz--Pimsner algebras constructed by Nekrashevych from self-similar actions and the GNS representations of the KMS states. The KMS states ... More
On Topologically Controlled Model Reduction for Discrete-Time SystemsMay 10 2019In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra ... More
On Topologically Controlled Model Reduction for Discrete-Time SystemsMay 10 2019May 19 2019In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra ... More
On Topologically Controlled Model Reduction for Discrete-Time SystemsMay 10 2019Jun 12 2019In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra ... More
Nets of graded $C^*$-algebras over partially ordered setsMay 09 2019The paper deals with $C^*$-algebras generated by a net of Hilbert spaces over a partially ordered set. The family of those algebras constitutes a net of $C^*$-algebras over the same set. It is shown that every such an algebra is graded by the first homotopy ... More
Some remarks in $C^*$- and $K$-theoryMay 09 2019This note consists of three unrelated remarks. First, we demonstrate how roughly speaking $*$-homomorphisms between matrix stable $C^*$-algebras are exactly the uniformly continuous $*$-preserving group homomorphisms between their genral linear groups. ... More
Conformal nets V: dualizabilityMay 09 2019We prove that finite-index conformal nets are fully dualizable objects in the 3-category of conformal nets. Therefore, assuming the cobordism hypothesis applies, there exists a local framed topological field theory whose value on the point is any finite-index ... More
Cuntz semigroups of ultraproduct C*-algebrasMay 08 2019We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the (ultra)product of a family of C*-algebras agrees with the (ultra)product ... More
Gabor Duality Theory for Morita Equivalent $C^*$-algebrasMay 06 2019The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalent $C^*$-algebras where the equivalence bimodule is a finitely generated projective Hilbert $C^*$-module. These ... More
Furstenberg boundary of minimal actionsMay 06 2019For a countable discrete group {\Gamma} and a minimal {\Gamma}-space X, we study the notion of ({\Gamma}, X)-boundary, which is a natural generalization of the notion of topological {\Gamma}-boundary in the sense of Furstenberg. We give characterizations ... More
Furstenberg boundary of minimal actionsMay 06 2019Jun 02 2019For a countable discrete group {\Gamma} and a minimal {\Gamma}-space X, we study the notion of ({\Gamma}, X)-boundary, which is a natural generalization of the notion of topological {\Gamma}-boundary in the sense of Furstenberg. We give characterizations ... More
Improvement on a Generalized Lieb's Concavity TheoremMay 04 2019We show that Lieb's concavity theorem holds more generally for any unitary invariant matrix function $\phi:\mathbf{H}_+^n\rightarrow \mathbb{R}_+^n$ that is concave and satisfies H\"older's inequality. Concretely, we prove the joint concavity of the function ... More
Radial operators on polyanalytic Bargmann-Segal-Fock spacesMay 02 2019The paper considers bounded linear radial operators on the polyanalytic Fock spaces $\mathcal{F}_n$ and on the true-polyanalytic Fock spaces $\mathcal{F}_{(n)}$. The orthonormal basis of normalized complex Hermite polynomials plays a crucial role in this ... More
On period, cycles and fixed points of a quantum channelMay 02 2019We consider a quantum channel acting on an infinite dimensional von Neumann algebra of operators on a separable Hilbert space. When there exists an invariant normal faithful state, the cyclic properties of such channels are investigated passing through ... More
Universal Block Tridiagonalization in B(H) and BeyondMay 02 2019For H a separable infinite dimensional complex Hilbert space, we prove that every B(H) operator has a basis with respect to which its matrix representation has a universal block tridiagonal form with block sizes given by a simple exponential formula independent ... More
Noncommutative versions of inequalities in quantum information theoryMay 02 2019In this paper, we aim to replace in the definitions of covariance and correlation the usual trace {\rm Tr} by a tracial positive map between unital $C^*$-algebras and to throw $x^{\alpha}$ and $x^{1-\alpha}$ in two functions $f$ and $g$ satisfying some ... More
Noncommutative versions of inequalities in quantum information theoryMay 02 2019May 11 2019In this paper, we aim to replace in the definitions of covariance and correlation the usual trace {\rm Tr} by a tracial positive map between unital $C^*$-algebras and to replace the functions $x^{\alpha}$ and $x^{1-\alpha}$ by functions $f$ and $g$ satisfying ... More
A canonical purification for the entanglement wedge cross-sectionMay 02 2019In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we ... More
Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-CategoriesMay 01 2019Generalized Temperley-Lieb-Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker. We introduce unitary modules for these generalized TLJ 2-categories as strong *-pseudofunctors into ... More
Fusion of implementers for spinors on the circleMay 01 2019We consider the space of odd spinors on the circle, and a decomposition into spinors supported on either the top or on the bottom half of the circle. If an operator preserves this decomposition, and acts on the bottom half in the same way as a second ... More
Extensions of the Lax-Milgram theorem to Hilbert C*-modulesApr 30 2019We present three versions of the Lax-Milgram theorem in the framework of Hilbert C*-modules, two for those over W*-algebras and one for those over C*-algebras of compact operators. It is remarkable that while the Riesz theorem is not valid for certain ... More
Dynamics of compact quantum metric spacesApr 30 2019We provide a detailed study of actions of the integers on compact quantum metric spaces, which includes general criteria ensuring that the associated crossed product algebra is again a compact quantum metric space in a natural way. We moreover provide ... More
Amenability and paradoxicality in semigroups and C*-algebrasApr 30 2019We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also F{\o}lner's type characterizations of amenability and give an example of a semigroup whose semigroup ... More
Noncommutative Geometry of Quantized CoveringsApr 30 2019May 21 2019This research is devoted to the noncommutative generalization of topological coverings. Otherwise since topological coverings are related to the set of geometric constructions one can obtain noncommutative generalizations of these constructions. Here ... More
Noncommutative Geometry of Quantized CoveringsApr 30 2019This research is devoted to the noncommutative generalization of topological coverings. Otherwise since topological coverings are related to the set of geometric constructions one can obtain noncommutative generalizations of these constructions. Here ... More
Good Wannier bases in Hilbert modules associated to topological insulatorsApr 30 2019For a large class of physically relevant operators on a manifold with discrete group action, we prove general results on the existence of a basis of smooth well-localised Wannier functions for their spectral subspaces. This turns out to be equivalent ... More
Aspects of $p$-adic operator algebrasApr 29 2019In this article, we propose a $p$-adic analogue of complex Hilbert space and consider generalizations of some well-known theorems from functional analysis and the basic study of operators on Hilbert spaces. We compute the $K$-theory of the analogue of ... More
State convertibility in the von Neumann algebra frameworkApr 29 2019We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite von Neumann algebras. Namely, we establish a generalisation to this setting ... More
Open projections and Murray-von Neumann equivalenceApr 27 2019We characterize the $C^\star$-algebras for which openness of projections in their second duals is preserved under Murray-von Neumann equivalence. They are precisely the extensions of the annihilator $C^\star$-algebras by the commutative $C^\star$-algebras. ... More