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Register a new userHypercyclic Sequences of weighted translations on hypergroups
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In this paper, we characterize hypercyclic sequences of weighted translation operators on an Orlicz space in the context of locally compact hypergroups.
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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.
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 Sturm-Liouville hypergroup with a positive index is $alpha$-amenable if and only if $alpha=1$.
We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the Cowling-Haagerup constant 1. As a corollary, we answer an open question of Eymard on Jacobi hypergroups. We also characterize the existence of bounded approximate identities for the hypergroup Fourier algebras of ultraspherical hypergroups.
In this paper, for a locally compact commutative hypergroup $K$ and for a pair $(Phi_1, Phi_2)$ of Young functions satisfying sequence condition, we give a necessary condition in terms of aperiodic elements of the center of $K,$ for the convolution $fast g$ to exist a.e., where $f$ and $g$ are arbitrary elements of Orlicz spaces $L^{Phi_1}(K)$ and $L^{Phi_2}(K)$, respectively. As an application, we present some equivalent conditions for compactness of a compactly generated locally compact abelian group. Moreover, we also characterize compact convolution operators from $L^1_w(K)$ into $L^Phi_w(K)$ for a weight $w$ on a locally compact hypergroup $K$.
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 the $alpha$-amenability of hypergroup joins and polynomial hypergroups in several variables as well as a single variable.
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