Characterization of multipliers on hypergroups

Abstract

Let K be a hypergroup. We characterize translation invariant operators from a vector-valued L¹-space to a vector-valued Lᵖ-space defined on K. Furthermore, for a commutative compact hypergroup A. we introduce and study the notion of character convolution transform of a Banach L¹(K)-module M. Several characterizations of multipliers on M are given. We also prove an analogue of the Schoenberg-Eberlein theorem for the character convolution transform.