Related papers: On compact Hankel operators over compact Abelian g…

In this paper we study harmonic analysis operators in Dunkl settings associated with finite reflection groups on Euclidean spaces. We consider maximal operators, Littlewood-Paley functions, $\rho$-variation and oscillation operators…

We develop the foundations of the theory of relatively geometric actions of relatively hyperbolic groups on CAT(0) cube complexes, a notion introduced in our previous work [5]. In the relatively geometric setting we prove: full relatively…

We characterize strong continuity of general operator semigroups on some Lebesgue spaces. In particular, a characterization of strong continuity of weighted composition semigroups on classical Hardy spaces and weighted Bergman spaces with…

There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture…

For a compact Hausdorff abelian group K and its subgroup H, one defines the g-closure g(H) of H in K as the subgroup consisting of $\chi \in K$ such that $\chi(a_n)\longrightarrow 0$ in T=R/Z for every sequence {a_n} in $\hat K$ (the…

How to extend Beurling's theorem on the shift invariant subspaces of Hardy class $H^2$ of the unit disk to several complex variables has been an open problem at least since 1964. In this paper, we prove a generalization of Beurling's…

For any countable torsion subgroup $H$ of an unbounded Abelian group $G$ there is a complete Hausdorff group topology $\tau$ such that $H$ is the von Neumann radical of $(G,\tau)$. In particular, any unbounded torsion countable Abelian…

This paper describes the $K$-theory structure for three algebra classes. For cyclic $p$-group rings and truncated polynomial rings over $\mathbb{Z}/p^s\mathbb{Z}$, we determine reduced $K_2$-structures via a common algebraic framework. For…

Given a set $A$ and an abelian group $B$ with operators in $A$, in the sense of Krull and Noether, we introduce the Ore group extension $B[x; \sigma_B, \delta_B]$ as the additive group $B[x]$, with $A[x]$ as a set of operators. Here, the…

A result of G. Pisier says that a convolution operator $\star f : M(G) \to C(G),$ where $G$ is a compact Abelian group, can be factored through a Hilbert space if and only if $f$ has the absolutely summable set of Fourier coefficients. P.…

The AH conjecture relates the low-dimensional homology groups of a groupoid with the abelianization of its topological full group. We show that transformation groupoids of minimal actions of the infinite dihedral group on the Cantor set…

We investigate pseudodifferential operators on arbitrary locally compact abelian groups. As symbol classes for the Kohn-Nirenberg calculus we introduce a version of Sjoestrand's class. Pseudodifferential operators with such symbols form a…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For compact operators $T$, we give a complete…

Let X be a compact Abelian group. In the article we obtain a characterization of shifts of Haar distributions on compact open subgroups of the group X by the symmetry of the conditional distribution of one linear form of independent random…

We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian…

We extend an old result of de la Harpe and Karoubi, concerning almost representations of compact groups, to proper groupoids admitting continuous Haar measure systems. As an application, we establish the existence of sufficiently many…

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…

Different notions of amenability on hypergroups and their relations are studied. Developing Leptin's theorem for discrete hypergroups, we characterize the existence of a bounded approximate identity for hypergroup Fourier algebras. We study…

Let $K$ be a field whose characteristic is prime to a fixed integer $n$ with $\mu_n \subset K$, and choose $\omega \in \mu_n$ a primitive $n$th root of unity. Denote the absolute Galois group of $K$ by $\operatorname{Gal}(K)$, and the…

We study the relationship between operator algebras, $C^*$ and von Neumann, acting on a Hilbert space and unitary representations of topological groups on the same space. We obtain certain correspondences between both these families of…