算子代数

Let $P$ be a closed convex cone in $\mathbb{R}^d$ which is assumed to be spanning $\mathbb{R}^d$ and contains no line. In this article, we consider a family of CAR flows over $P$ and study the decomposability of the associated product…

We survey the symmetry preserving properties for the dual propinquity, under natural non-degeneracy and equicontinuity conditions. These properties are best formulated using the notion of the covariant propinquity when the symmetries are…

In this work, we solve the problem explicitly stated at the end of a paper of Junge, Mei and Parcet [JEMS2018, Problem C.5] for a large class of groups including all amenable groups and free groups. More precisely, we prove that the…

We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the…

Suppose A and B are unital C*-algebras and A is separable. Let Rep(A,B) denote the set of all unital *-homomorphisms from A to B with the topology of pointwise convergence. We consider the problem of when the closure of the unitary orbit of…

Consider an arbitrary extension of a free $\mathbb Z^d$-action on the Cantor set. It is shown that it has dynamical asymptotic dimension at most $3^d - 1$.

Let $(X, \Gamma)$ be a free and minimal topological dynamical system, where $X$ is a separable compact Hausdorff space and $\Gamma$ is a countable infinite discrete amenable group. It is shown that if $(X, \Gamma)$ has the Uniform Rokhlin…

We prove that the $L^2$-Betti numbers of a rigid $C^*$-tensor category vanish in the presence of an almost-normal subcategory with vanishing $L^2$-Betti numbers, generalising a result of Bader, Furman and Sauer. We apply this criterion to…

Let $(X, \Gamma)$ be a free minimal dynamical system, where $X$ is a compact separable Hausdorff space and $\Gamma$ is a discrete amenable group. It is shown that, if $(X, \Gamma)$ has a version of Rokhlin property (uniform Rokhlin…

In this paper, we connect the rigidity problem and the coarse Baum-Connes conjecture for Roe algebras. In particular, we show that if $X$ and $Y$ are two uniformly locally finite metric spaces such that their Roe algebras are…

We define a representation of the unitary group $U(n)$ by metaplectic operators acting on $L^2(\mathbb{R}^n)$ and consider the operator algebra generated by the operators of the representation and pseudodifferential operators of Shubin…

Tiling spaces are constructed using a metric in which two tilings of $\mathbb{R}^n$ are close if and only if, after a small translation, they agree on a large ball around the origin. We construct analogous spaces to study random…

In our attempt to explore how the quantum nonstandard complex projective spaces $\mathbb{C}P_{q,c}^{n}$ studied by Korogodsky, Vaksman, Dijkhuizen, and Noumi are related to those arising from the geometrically constructed Bohr-Sommerfeld…

We consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an…

Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…

Given a Lie group $G$ of quantized canonical transformations acting on the space $L^2(M)$ over a closed manifold $M$, we define an algebra of so-called $G$-operators on $L^2(M)$. We show that to $G$-operators we can associate symbols in…

In the present work we study elliptic operators on manifolds with singularities in the situation, when the manifold is endowed with an action of a discrete group $G$. As usual in elliptic theory, the Fredholm property of an operator is…

We define Atiyah-Bott index on stratified manifolds and express it in topological terms. By way of example, we compute this index for geometric operators on manifolds with edges.

In this paper, we consider a simple test case of multiparameter product systems that arise out of random measures. We associate a product system to a stationary Poisson process and a stationary compound Poisson process. We show that the…

We study the connection between the Baum-Connes conjecture for an ample groupoid $G$ with coefficient $A$ and the K\"unneth formula for the K-theory of tensor products by the crossed product $A\rtimes_r G$. To do so we develop the machinery…