Disjointness preserving maps between vector-valued group algebras

Abstract

Let G be a locally compact abelian group and B be a commutative Banach algebra. Let $$L^{1}(G, B)$$ be the Banach algebra of B-valued Bochner integrable functions on G. In this paper we provide a complete description of continuous disjointness preserving maps on $$L^{1}(G, B)$$ -algebras based on a scarcely used tool: the vector-valued Fourier transform. We also present necessary and sufficient conditions for these operators to be compact.