2021/09/08 by Simone Di Marino, Di Marino, Simone, Danka Lučić +3 · 1 citation
Mathematics · #13C05 #18F15 #28A51 #30L05 #46G15 #53C23 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2109.03509
openalex publication_date 2021/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.