Duals and pullbacks of normed modules

Abstract

We give a general description of the dual of the pullback of a normed module. Ours is the natural generalization to the context of modules of the well-known fact that the dual of the Lebesgue-Bochner space $L^p([0,1],B)$ consists - quite roughly said - of $L^q$ maps from $[0,1]$ to the dual $B^{\prime }$ of $B$ equipped with the weak${}^{\ast }$ topology. In order to state our result, we study various fiberwise descriptions of a normed module that are of independent interest.

35 pages

References in corpus (1)

• Recent progress in random metric theory and its applications to conditional risk measures