On reflexivity of the Bochner space L-P (mu, E) for arbitrary mu

Abstract

Let (Omega, A, mu) be a finite positive measure space, E a Banach space, and 1 < p < infinity. It is known that the Bochner space L-P (mu, E) is reflexive if and only if E is reflexive. It is also known that L(L-1(mu), E) = L-infinity (mu, E) if and only if E has the Radon-Nikodym property. In this study, as an application of hyperstonean spaces, these results are extended to arbitrary measures by replacing the given measure space by an equivalent perfect one.