Related papers: Wreath products with the integers, proper actions …
The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces $\mathcal{H}_K$ on the unit ball in $\mathbb…
We show that the elasticity Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…
We show that an equation follows from the axioms of dagger compact closed categories if and only if it holds in finite dimensional Hilbert spaces.
We find bounds on the Hilbert space compression of the limit of a directed metric system of groups. We also give estimates on the Hilbert space compression of group extensions of a group $H$ by a a word-hyperbolic group or a group of…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
To a finite group G one can associate a tower of wreath products S_n[G]. It is well known that the graded direct sum of the Grothendieck groups of the categories of finite dimensional complex representations of these groups can be given the…
We show that amenability, the Haagerup property, the Kazhdan's property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of groups, this is a…
Given the large class of groups already known to be sofic, there is seemingly a shortfall in results concerning their permanence properties. We address this problem for wreath products, and in particular investigate the behaviour of more…
If $\mathcal{H}$ denotes a Hilbert space of analytic functions on a region $\Omega \subseteq \mathbb{C}^d$, then the weak product is defined by $$\mathcal{H}\odot\mathcal{H}=\left\{h=\sum_{n=1}^\infty f_n g_n : \sum_{n=1}^\infty…
We use deformation-rigidity theory in von Neumann algebra framework to study probability measure preserving actions by wreath product groups. In particular, we single out large families of wreath products groups satisfying various type of…
We prove that the image of an elliptic operator on a smooth separable Hilbert fibre bundle on compact manifolds is closed with respect to the natural pre-Hilbert topology. We consider a tensor product of the operator, which is invariant…
Sub-Bergman Hilbert spaces are analogues of de Branges-Rovnyak spaces in the Bergman space setting. They are reproducing kernel Hilbert spaces contractively contained in the Bergman space of the unit disk. K. Zhu analyzed sub-Bergman…
We show that several known results about the algebraic K-theory of tensor products of algebras with the C*-algebra of compact operators in Hilbert space remain valid for tensor products with any properly infinite C*-algebra.
We shall prove that the Hilbert cube cannot be separated by a weakly infinite dimensional subset. As a corollary we obtain that the complement of a weakly infinite dimensional subset of the space of complete non negatively curved metrics is…
We show that for $X$ a proper $\mathrm{CAT}(-1)$ space there is a maximal open subset of the horofunction compactification of $X\times X$ with respect to the maximum metric that compactifies the diagonal action of an infinite quasi-convex…
Given a w*-closed unital algebra $A$ acting on $H_0$ and a contractive w*-continuous endomorphism $\beta$ of $A$, there is a w*-closed (non-selfadjoint) unital algebra $\mathbb{Z}_+\bar{\times}_\beta A$ acting on…
If one tries to embed a metric space uniformly in Hilbert space, how close to quasi-isometric could the embedding be? We answer this question for finite dimensional CAT(0) cube complexes and for hyperbolic groups. In particular, we show…
Let $X$ be an infinite compact metric space with finite covering dimension and let $\alpha, \beta : X\to X$ be two minimal homeomorphisms. We prove that the crossed product $C^*$-algebras $C(X)\rtimes_\alpha\Z$ and $C(X)\rtimes_\belta\Z$…
We prove the following rank rigidity result for proper CAT(0) spaces with one-dimensional Tits boundaries: Let $\Gamma$ be a group acting properly discontinuously, cocompactly, and by isometries on such a space $X$. If the Tits diameter of…
We study w*-semicrossed products over actions of the free semigroup and the free abelian semigroup on (possibly non-selfadjoint) w*-closed algebras. We show that they are reflexive when the dynamics are implemented by uniformly bounded…