Work

Representation theorems for normed modules

Year: 2024

Type: article

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.

Source: Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas

DOI: 10.1007/s13398-024-01682-0

Authors: Simone Di Marino, Danka Lučić, Enrico Pasqualetto

Institutions: University of Genoa, University of Pisa, Scuola Normale Superiore

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Jyväskylän Yliopisto, Air Force Office of Scientific Research