C∗-algebra structure on vector valued-Banach algebras.

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 ∞ (X , A) . We prove that these algebras are isomorphic with a C ∗ -algebra if and only if A is so. [ABSTRACT FROM AUTHOR]