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.
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J.J. Font is supported by Spanish Government (MTM2016-77143-P), Universitat Jaume I (Projecte P11B2014-35) and Generalitat Valenciana (Projecte AICO/2016/030).
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Hosseini, M., Font, J.J. Disjointness preserving maps between vector-valued group algebras. Aequat. Math. 92, 549–561 (2018). https://doi.org/10.1007/s00010-018-0547-6
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DOI: https://doi.org/10.1007/s00010-018-0547-6