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A matrix convex set is a set of the form $\mathcal{S} = \cup_{n\geq 1}\mathcal{S}_n$ (where each $\mathcal{S}_n$ is a set of $d$-tuples of $n \times n$ matrices) that is invariant under UCP maps from $M_n$ to $M_k$ and under formation of…

Complete Pick algebras - these are, roughly, the multiplier algebras in which Pick's interpolation theorem holds true - have been the focus of much research in the last twenty years or so. All (irreducible) complete Pick algebras may be…

We show that (central) Cowling-Haagerup constant of discrete quantum groups is multiplicative, which extends the result of Freslon to general (not necesarilly unimodular) discrete quantum groups. The crucial feature of our approach is…

We introduce the notion of a $\mathbb{G}$-operator space $(X, \alpha)$, which consists of an action $\alpha: X \curvearrowleft \mathbb{G}$ of a locally compact quantum group $\mathbb{G}$ on an operator space $X$, and we make a study of the…

We describe the primitive ideal spaces and the Jacobson topologies of a special class of topological graph algebras.

Let $\mathbb{G}$ be a compact quantum group and $A\subseteq B$ an inclusion of $\sigma$-finite $\mathbb{G}$-dynamical von Neumann algebras. We prove that the $\mathbb{G}$-inclusion $A\subseteq B$ is strongly equivariantly amenable if and…

Let $S$ be a complete operator system with a generating cone; i.e. $S_\sa = S_+ - S_+$. We show that there is a matrix norm on the dual space $S^*$, under which, and the usual dual matrix cone, $S^*$ becomes a dual operator system with a…

We show that the space of trace-class operators on a Hilbert module over a commutative C*-algebra, as defined and studied in earlier work of Stern and van Suijlekom (Journal of Functional Analysis, 2021), is completely isometrically…

We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial…

We show an isomorphism between the kernel of the C*-algebra of the tangent groupoid of a filtered manifold and the crossed product of the order 0 pseudodifferential operators in the associated filtered calculus by a natural R-action. This…

We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.

We study a generalization of free Poisson random measure by replacing the intensity measure with a n.s.f. weight $\varphi$ on a von Neumann algebra $M$. We give an explicit construction of the free Poisson random weight using full Fock…

Let $X$ be a compact metrizable space, and let $\Delta$ be a closed set of Borel probability measures on $X$. We study the small boundary property of the pair $(X, \Delta)$. In particular, it is shown that $(X, \Delta)$ has the small…

We find a subtle modification to the construction of Chifan-Ioana-Kunnawalkam Elayavalli, which yields a drastic simplification of the proof of the existence of two non Gamma non elementarily equivalent II$_1$ factors.

Voiculescu's notion of asymptotic free independence applies to a wide range of random matrices, including those that are independent and unitarily invariant. In this work, we generalize this notion by considering random matrices with a…

A hereditarily atomic von Neumann algebra $A$ is a $W^*$ product of matrix algebras, regarded as the underlying function algebra of a quantum set. Projections in $A\overline{\otimes}A^{\circ}$ are interpreted as quantum binary relations on…

Motivated by classical investigation of conjugation invariant positive-definite functions on discrete groups, we study tracial central states on universal C*-algebras associated with compact quantum groups, where centrality is understood in…

Let $\mathcal{G}$ be a quantum graph without quantum sources and $E_\mathcal{G}$ be the quantum edge correspondence for $\mathcal{G}.$ Our main results include sufficient conditions for simplicity of the Cuntz-Pimsner algebra…

We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima-Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity and…

We introduce the notion of the weak Brehmer's condition and prove that the Cauchy transform for a representation of a right-angled Artin monoid is bounded under such conditions. As a result, we obtain the Poisson transform and $*$-regular…