(L_{1}\)- Properties of vector-valued Banach algebras

Let \(G\) be a locally compact group and \(A\) be a commutative semisimple Banach algebra over the scalar field \(\mathbb{C}\). The correlation between different types of \(BSE\)- Banach algebras \(A\), and the Banach algebras \(L^{1}(G, A)\) are assessed. It is found and approved that \(M(G, A) = L...

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Published in:arXiv.org 2022-12
Main Authors: Aghakoochaki, Maryam, Rejali, Ali
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Algebra
Banach spaces
Fields (mathematics)
Group theory
Scalars
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description Let \(G\) be a locally compact group and \(A\) be a commutative semisimple Banach algebra over the scalar field \(\mathbb{C}\). The correlation between different types of \(BSE\)- Banach algebras \(A\), and the Banach algebras \(L^{1}(G, A)\) are assessed. It is found and approved that \(M(G, A) = L^{1}(G, A)\) if and only if \(G\) is discrete. Furthermore, some properties of vector-valued measure algebras on groups are given, so that \(M(G, A)\) is a convolution measure algebra.
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subjects Algebra
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Group theory
Scalars
title (L_{1}\)- Properties of vector-valued Banach algebras
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