Disjointness preserving maps between vector-valued group algebras

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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.

Keywords

Locally compact abelian group Vector-valued group algebras Disjointness preserving mappings 

Mathematics Subject Classification

Primary 47B38 Secondary 43A20 43A22 43A25 
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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of MathematicsK. N. Toosi University of TechnologyTehranIran
  2. 2.Departamento de Matemáticas (IMAC)Universitat Jaume ICastellónSpain

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