$C^{\ast}-$algebra structure on vector valued-Banach algebras
Ali Rejali, Mitra Amiri

TL;DR
This paper characterizes when certain vector valued Banach algebras, constructed from a commutative semisimple Banach algebra, are isomorphic to a C*-algebra, based on the properties of the algebra A.
Contribution
It establishes a necessary and sufficient condition for vector valued Banach algebras to be C*-algebras, extending the understanding of their algebraic structure.
Findings
Vector valued Banach algebras are C*-algebras if and only if A is a C*-algebra.
Isomorphism conditions are established for $C_0(X,A)$, $L^p(G,A)$, $l^p(X,A)$, and $l^{ abla}(X,A)$.
The results unify the structure theory of these algebras under the C*-algebra framework.
Abstract
Let be a commutative semisimple Banach algebra, be a locally compact Hausdorff topological space and be a locally compact topological group. In this paper, we investigate several properties of vector valued Banach algebras , , and . We prove that these algebras are isomorphic with a algebra if and only if is so.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Operator Algebra Research · Advanced Topics in Algebra
