Representation theorems for normed modules
Functional Analysis
2021-09-09 v1 Differential Geometry
Metric Geometry
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.
Cite
@article{arxiv.2109.03509,
title = {Representation theorems for normed modules},
author = {Simone Di Marino and Danka Lučić and Enrico Pasqualetto},
journal= {arXiv preprint arXiv:2109.03509},
year = {2021}
}
Comments
46 pages