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arXiv · 2201.00793

$C^{\ast}-$algebra structure on vector valued-Banach algebras

Ali Rejali·Mitra Amiri
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Abstract

Let $A$ be a commutative semisimple Banach algebra, $X$ be a locally compact Hausdorff topological space and $G$ be a locally compact topological group. In this paper, we investigate several properties of vector valued Banach algebras $C_0(X,A)$, $L^p(G,A)$, $l^p(X,A)$ and $l^{\infty}(X,A)$. We prove that these algebras are isomorphic with a $C^*-$algebra if and only if $A$ is so.

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Ali Rejali, Mitra Amiri. 2022-01-03. $C^{\ast}-$algebra structure on vector valued-Banach algebras. https://arxiv.org/abs/2201.00793

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