Publication

Abstract : This article is intended towards the study of the bidual of generalized group algebra L 1 ( G , A ) equipped with two Arens products, where G is any locally compact group and A is a Banach algebra. We show that the left topological center of ( L 1 ( G ) ⊗ ˆ A ) ⁎ ⁎ is a Banach L 1 ( G ) -module if G is abelian. Further it also holds permanence property with respect to the unitization of A . We then use this fact to extend the remarkable result of A.M. Lau and V. Losert [7], about the topological center of L 1 ( G ) ⁎ ⁎ being just L 1 ( G ) , to the reflexive Banach algebra valued case using the theory of vector measures. We further explore pseudo-center of L 1 ( G , A ) ⁎ ⁎ for non-reflexive Banach algebras A and give a partial characterization for elements of pseudo-center using the Cohen's factorization theorem. In the running we also observe few consequences when A holds the Radon-Nikodym property and weak sequential completeness.