On the smoothness of L p of a positive vector measure

Abstract

We investigate natural sufficient conditions for a space L p(m) of pintegrable functions with respect to a positive vector measure to be smooth. Under some assumptions on the representation of the dual space of such a space, we prove that this is the case for instance if the Banach space where the vector measure takes its values is smooth. We give also some examples and show some applications of our results for determining norm attaining elements for operators between two spaces L p(m1) and Lq (m2) of positive vector measures m1 and m2.