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arXiv · 2109.03509

Representation theorems for normed modules

Simone Di Marino·Danka Lučić·Enrico Pasqualetto
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Abstract

In this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework of normed modules, thus providing a notion of precise representative of their elements; to prove that each separable normed module can be represented as the space of sections of a measurable Banach bundle. By combining our representation result with Gigli's differential structure, we eventually show that every metric measure space (whose Sobolev space is separable) is associated with a cotangent bundle in a canonical way.

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Simone Di Marino, Danka Lučić, Enrico Pasqualetto. 2021-09-08. Representation theorems for normed modules. https://arxiv.org/abs/2109.03509

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