Duals and pullbacks of normed modules

2022/07/11 by Nicola Gigli, Gigli, Nicola, Danka Lučić +3 · 3 citations
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2207.04972

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' of B equipped with the weak^* topology. In order to state our result, we study various fiberwise descriptions of a normed module that are of independent interest.

Cited by

• The random Kakutani fixed point theorem in random normed modules
• Tensor products of measurable Banach bundles
• A new complete proof of the random Brouwer fixed point theorem and its implied consequences of unification

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• Direct and inverse limits of normed modules
• Representation theorems for normed modules
• An axiomatic theory of normed modules via Riesz spaces
• A note on the 2-dual space of L^p[0,1]
• The Serre-Swan theorem for normed modules