On the reflexivity properties of Banach bundles and Banach modules

In this paper, we investigate some reflexivity-type properties of separable measurable Banach bundles over a s-finite measure space. Our two main results are the following: center dot The fibers of a bundle are uniformly convex (with a commonmodulus of convexity) if and only if the space of its L-p-sections is uniformly convex for every p is an element of (1,infinity). center dot The fibers of a bundle are reflexive if and only if the space of its L-p-sections is reflexive for every p is an element of (1,infinity). They generalise well-known results for Lebesgue-Bochner spaces.