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Katsura associated a $C^*$-algebra $C^*_{A,B}$ to integral matrices $A\ge 0$ and $B$ of the same size, gave sufficient conditions on $(A,B)$ making it simple purely infinite (SPI), and proved that any separable $C^*$-algebra $KK$-isomorphic…

We characterize Beurling quotient subspaces for pure doubly commuting isometric representations of product systems. As a consequence, we derive a concrete regular dilation theorem for a pure completely contractive covariant representation…

We obtain Berger-Coburn-Lebow (BCL)-representation for pure isometric covariant representation of product system over $\mathbb{N}_0^2$. Then the corresponding complete set of (joint) unitary invariants is studied, and the BCL-…

This paper concerns the non-commutative analog of the Normal Subgroup Theorem for certain groups. Inspired by Kalantar-Panagopoulos, we show that all $\Gamma$-invariant subalgebras of $L\Gamma$ and $C^*_r(\Gamma)$ are ($\Gamma$-)…

A group is called matricial field (MF) if it admits finite dimensional approximate unitary representations which are approximately faithful and approximately contained in the left regular representation. This paper provides a new class of…

We provide a Hunt type formula for the infinitesimal generators of L\'evy process on the quantum groups $SU_q(N)$ and $U_q(N)$. In particular, we obtain a decomposition of such generators into a gaussian part and a `jump type' part…

Given an inclusion of II$_1$ factors $N\subset M$ with finite Jones index, $[M:N]<\infty$, we prove that for any $F\subset M$ finite and $\varepsilon >0$, there exists a partition of $1$ with $r\leq \lceil 16\varepsilon^{-2}\rceil$ $\cdot…

We investigate Matui-Sato's notion of property (SI) for C*-dynamics, this time with a focus on actions of possibly non-amenable groups. The main result is a generalization of earlier work: For any countable group $\Gamma$ and any…

Olofsson introduced a growth condition regarding elements of an orbit for an expansive operator and generalized Richter's wandering subspace theorem. Later on, using the Moore-Penrose inverse, Ezzahraoui, Mbekhta, and Zerouali extended the…

The set of states on ${\rm CCR}(\ch)$, the CCR algebra of a separable Hilbert space $\ch$, is here looked at as a natural object to obtain a non-commutative version of Freedman's theorem for unitarily invariant stochastic processes. In this…

In this paper, we construct large subalgebras of crossed product C*-algebras of noncommutative C*-dynamics from ideals. We apply our results to study locally trivial unital $C(X)$-algebras such as mapping tori.

Let $\Omega$ be a class of unital $\rm C^{*}$-algebras. The class of ${\rm C^*}$-algebras which are asymptotical tracially in $\Omega$, denoted by ${\rm AT}\Omega$. In this paper, we will show that the following class of ${\rm…

We review some results on spreadable quantum stochastic processes and present the structure of some monoids acting on the index-set of all integers $\mathbb Z$. These semigroups are strictly related to spreadability, as the latter can be…

Conformal Quantum Field Theories (CFT) in 1 or 1+1 spacetime dimensions (respectively called chiral and full CFTs) admit several "axiomatic" (mathematically rigorous and model-independent) formulations. In this note, we deal with the von…

This note aims to study the iteration theory of noncommutative self-maps of bounded matrix convex domains. We prove a version of the Denjoy-Wolff theorem for the row ball and the maximal quantization of the unit ball of $\mathbb{C}^d$. For…

We study the gauge-invariant ideal structure of the Nica-Toeplitz algebra $\mathcal{NT}(X)$ of a product system $(A, X)$ over $\mathbb{N}^n$. We obtain a clear description of $X$-invariant ideals in $A$, that is, restrictions of…

We show that the convolution algebra of smooth, compactly-supported functions on a Lie groupoid is H-unital in the sense of Wodzicki. We also prove H-unitality of infinite order vanishing ideals associated to invariant, closed subsets of…

We introduce the notion of self-similar actions of grouopids on other groupoids and Fell bundles. This leads to a new imprimitivity theorem arising from such dynamics, generalizing many earlier imprimitivity theorems involving group and…

We show that for C*-algebras with the Global Glimm Property, the rank of every operator can be realized as the rank of a soft operator, that is, an element whose hereditary sub-C*-algebra has no nonzero, unital quotients. This implies that…

Building on work of Williams, Wieler proved that every irreducible Smale space with totally disconnected stable sets can be realized via a stationary inverse limit. Using this result, the first and fourth listed authors of the present paper…