Geometric properties of some Banach spaces on hypergroups

Abstract

In this paper, we study some geometric properties of the Fourier space of a hypergroup and other related Banach spaces. We are mainly concerned with the Radon-Nikodym property, the Dunford-Pettis property and the Schur property. Among other results, we proved that if H is a commutative hypergroup, then the Fourier space of A(H) has the Dunford-Pettis property; if $H$ is a compact hypergroup then A(H) has the Schur property and consequently the Dunford-Pettis property. We also showed that the Figa-Talamanca--Herz space A_p(H) does not have the Schur property if H is not compact.