算子代数

We establish a hypertrace characterization of property (T) for $\mathrm{II}_1$ factors: Given a $\mathrm{II}_1$ factors $M$, $M$ does not have property (T) if and only if there exists a von Neumann algebra $\mathcal{A}$ with $M\subset…

We investigate the liberation question for the compact Lie groups, by using various "soft" and "hard" methods, based respectively on joint generation with a free quantum group, and joint generation with a free torus. The soft methods extend…

In this paper, we introduce a notion of transfinite nuclear dimension for $C^*$-algebras, which coincides with the nuclear dimension when taking values in natural numbers. We use it to characterise a stronger form of having nuclear…

Using Araki-Yamagami's characterization of quasi-equivalence for quasi-free representations of the CCRs, we provide an abstract criterion for the existence of isomorphisms of second quantization local von Neumann algebras induced by…

We introduce the notion of an action of a discrete or compact quantum group on an operator system, and study equivariant operator system injectivity. We then prove a duality result that relates equivariant injectivity with dual injectivity…

We characterise subhomogeneity for twisted \'etale groupoid C*-algebras and obtain an upper bound on their nuclear dimension. As an application, we remove the principality assumption in recent results on upper bounds on the nuclear…

Let $\alpha : \Gamma \curvearrowright A$ be an action of a discrete group $\Gamma$ on a unital C*-algebra $A$ by *-automorphisms and let $A \rtimes_{\alpha,\lambda} \Gamma$ denote the corresponding reduced crossed product C*-algebra.…

Let $R_\infty$ denote the Araki--Woods factor -- the unique separable injective type III$_{1}$ factor. For extremal almost periodic states $\varphi, \psi\in (R_\infty)_*$, we show that if $\Delta_\varphi$ and $\Delta_\psi$ have the same…

We define and study the external and the internal Zappa-Sz\'{e}p product of twists over groupoids. We determine when a pair $(\Sigma_{1},\Sigma_{2})$ of twists over a matched pair $(\mathcal{G}_{1},\mathcal{G}_{2})$ of groupoids gives rise…

We study different types of von Neumann algebras arising from the Connes-Marcolli $GSp_4$-system and show that a phase transition occurs at the level of these algebras. More precisely, we show that the type of these algebras transitions…

We extend theorems of Breuillard-Kalantar-Kennedy-Ozawa on unital reduced crossed products to the non-unital case under mild assumptions. As a result simplicity of C*-algebras is stable under taking reduced crossed product over discrete…

Given a locally compact \'etale groupoid and an ideal $I$ in its groupoid C$^*$-algebra, we show that $I$ defines a family of ideals in group C$^*$-algebras of the isotropy groups and then study to which extent $I$ is determined by this…

Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be a maximal subdiagonal subalgebra of $\mathcal{M}$. We have proved that for $0< p<1$, $H^p(\mathcal{A})$ is…

Nevanlinna-Herglotz functions play a fundamental role for the study of infinitely divisible distributions in free probability. In the present paper we study the role of the tangent function, which is a fundamental Herglotz-Nevanlinna…

We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of…

We study subordination of free convolutions. We prove that for free random variables $X,Y$ and a Borel function $f$ the conditional expectation $E_\varphi\left[ (z-X-f(X)Yf^*(X))^{-1}| X\right]$, is a resolvent again. This result allows…

We define spreadability systems as a generalization of exchangeability systems in order to unify various notions of independence and cumulants known in noncommutative probability. In particular, our theory covers monotone independence and…

In this paper we study multiplication operators on Bergman spaces of high dimensional bounded domains and those von Neumann algebras induced by them via the geometry of domains and function theory of their symbols. In particular, using…

In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of…

This paper explores the concept of $K$-$g$-frames in locally $C^*$-algebras, which are shown to be more general than $g$-frames. The authors first introduce the notion of a $g$-orthonormal basis and utilize it to define the $g$-operator, a…