English

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

Functional Analysis 2022-01-04 v1

Abstract

Let AA be a commutative semisimple Banach algebra, XX be a locally compact Hausdorff topological space and GG be a locally compact topological group. In this paper, we investigate several properties of vector valued Banach algebras C0(X,A)C_0(X,A), Lp(G,A)L^p(G,A), lp(X,A)l^p(X,A) and l(X,A)l^{\infty}(X,A). We prove that these algebras are isomorphic with a CC^*-algebra if and only if AA is so.

Keywords

Cite

@article{arxiv.2201.00793,
  title  = {$C^{\ast}-$algebra structure on vector valued-Banach algebras},
  author = {Ali Rejali and Mitra Amiri},
  journal= {arXiv preprint arXiv:2201.00793},
  year   = {2022}
}
R2 v1 2026-06-24T08:38:57.571Z