Some geometric properties on the Fourier and Fourier-Stieltjes algebras of locally compact groups, Arens regularity and related problems

Abstract

Let G be a locally compact topological group and A(G) [B(G)] be, respectively, the Fourier and Fourier-Stieltjes algebras of G. It is one of the purposes of this paper to investigate the RNP (= Radon-Nikodym property) and some other geometric properties such as weak RNP, the Dunford-Pettis property and the Schur property on the algebras A(G) and B(G), and to relate these properties to the properties of the multiplication operator on the group C*-algebra C*(G). We also investigate the problem of Arens regularity of the projective tensor products C*(G)⊗A, when B(G) = C*(G)* has the RNP and A is any C*-algebra. Some related problems on the measure algebra, the group algebra and the algebras A p (G), PF p (G), PM p (G) (1 < p < ∞) are also discussed