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Weighted group algebras have been studied extensively in Abstract Harmonic Analysis where complete characterizations have been found for some important properties of weighted group algebras, namely amenability and Arens regularity. One of the generalizations of weighted group algebras is weighted hypergroup algebras. Defining weighted hypergroups, analogous to weighted groups, we study Arens regularity and isomorphism to operator algebras for them. We also examine our results on three classes of discrete weighted hypergroups constructed by conjugacy classes of FC groups, the dual space of compact groups, and hypergroup structure defined by orthogonal polynomials. We observe some unexpected examples regarding Arens regularity and operator isomorphisms of weighted hypergroup algebras.
In this paper, we characterize hypercyclic sequences of weighted translation operators on an Orlicz space in the context of locally compact hypergroups.
Let $K$ denote a locally compact commutative hypergroup, $L^1(K)$ the hypergroup algebra, and $alpha$ a real-valued hermitian character of $K$. We show that $K$ is $alpha$-amenable if and only if $L^1(K)$ is $alpha$-left amenable. We also consider
We investigate an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters. We assume that each cluster is composed of identical units (monomers) and we allow mass to be lost, gained or conserved du
Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfactors, possibly with infinite Jones index if one takes non-rational th
Let $UC(K)$ denote the Banach space of all bounded uniformly continuous functions on a hypergroup $K$. The main results of this article concern on the $alpha$-amenability of $UC(K)$ and quotients and products of hypergroups. It is also shown that a S