Bochner algebras and their compact multipliers

Abstract

Let A{fraktur} be a normed algebra with identity, Ω be a locally compact Hausdorf space and λ be a positive Radon measure on Ω with supp(λ) = Ω. In this paper, we establish a necessary and sufficient condition for L 1(Ω, A{fraktur}) to be an algebra with pointwise multiplication. Under this condition, we then characterize compact and weakly compact left multipliers on L 1(Ω, A{fraktur}). © 2012 Versita Warsaw and Springer-Verlag Wien.