算子代数
We prove the following operator-coefficients free Poincar\'{e} inequality: $$|f(X)-E[f(X)]|_{2}\leq2|X|_{2}\|\widehat{\partial}_{X:B}[f(X)]\|_{\pi}, \quad f(X) \in \mathrm{dom}(\widehat{\partial}_{X:B}),$$ where $\|\cdot\|_{\pi}$ is the…
We study the closure of the unitary orbit of a given point in the non-commutative Choquet boundary of a unital operator space with respect to the topology of pointwise norm convergence. This may be described more extensively as the…
Let $\IM =\otimes_{n \in \IZ}\!M^{(n)}(\IC)$ be the two sided infinite tensor product $C^*$-algebra of $d$ dimensional matrices $\!M^{(n)}(\IC)=\!M_d(\IC)$ over the field of complex numbers $\IC$ and $\omega$ be a translation invariant…
Based on the observation that Cacic [10]'s characterization of almost commutative spectral triples as Clifford module bundles can be pushed to endomorphim algebras of Dirac bundles, with the geometric Dirac operator related to the Dirac…
In this article we study analogues of the weak expectation property of discrete group C*-algebras and their crossed products, in the discrete quantum group setting, i.e., discrete quantum group C*-algebras and crossed products of…
Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete…
We investigate quantum lens spaces, $C(L_q^{2n+1}(r;\underline{m}))$, introduced by Brzezi\'nski-Szyma\'nski as graph $C^*$-algebras. We give a new description of $C(L_q^{2n+1}(r;\underline{m}))$ as graph $C^*$-algebras amending an error in…
A row co-isometry is a family $(V_i)_{i=0}^{N-1}$ of operators on a Hilbert space, subject to the relation $$\sum_{i=0}^{N-1}V_iV_i^*=I.$$ As shown in \cite{BJK00}, row co-isometries appear as compressions of representations of Cuntz…
We study the noncommutative topology of the $C^*$-algebras $C(\mathbb{C}P_q^{n})$ of the quantum projective spaces within the framework of Kasparov's bivariant K-theory. In particular, we construct an explicit KK-equivalence with the…
We study the Brown measure of certain non-hermitian operators arising from Voiculescu's free probability theory. Usually those operators appear as the limit in *-moments of certain ensembles of non-hermitian random matrices, and the Brown…
We develop a fundamental theory of compact quantum group equivariant finite extensions of C*-algebras. In particular we focus on the case of quantum homogeneous spaces and give a Tannaka-Krein type result for equivariant correspondences. As…
For an $m \times n$ complex matrix $X$ of rank $r$ with Schur multiplier $S_X$ we show that there exist an $ r \times m $ complex matrix $L$ and an $ r\times n $ complex matrix $R$ such that $X = L^*R$ and $\|S_X\|\, =\, \|\mathrm{diag}…
We characterize the ideals of the semicrossed product $C_0(X) \times_\phi \mathbb{Z}_+$ with left (resp. right) approximate unit.
We show that, when $A$ is a separable C*-algebra, every countably generated Hilbert $A$-module is projective (with bounded module maps as morphisms). We also study the approximate extensions of bounded module maps. In the case that $A$ is a…
Let $E=E(0,\infty)$ be a symmetric function space and $E(\mathcal{M},\tau)$ be a symmetric operator space associated with a semifinite von Neumann algebra with a faithful normal semifinite trace. Our main result identifies the class of…
We give a new alternative version of the reconstruction procedure for ergodic actions of compact quantum groups and we refine it to include characterizations of (braided commutative) Yetter-Drinfeld C*-algebras. We then use this to…
We give a simple and complete picture on the classification of relative Cuntz--Pimsner algebras (and so also of gauge-equivariant representations) using their intuitive parametrisation by kernel--covariance pairs.
Marc Rieffel had introduced the notion of the quantum Gromov-Hausdorff distance on compact quantum metric spaces and found a sequence of matrix algebras that converges to the space of continuous functions on $2$-sphere in this distance. One…
We study the question whether the representations defined by a dense subset of the unit space of a locally compact \'etale groupoid are enough to determine the reduced norm on the groupoid C$^*$-algebra. We present sufficient conditions for…
This paper is devoted to the study of pointwise convergence of Fourier series for group von Neumann algebras and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as summation methods…