2023/06/21 by Danka Lučić, Lučić, Danka, Enrico Pasqualetto +1 · 1 citation
Computer Science · Mathematics · #06F20 #13C05 #46A40 #53C23 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2306.12238
openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study an axiomatic theory of V-normed U-modules, where V is a Riesz space and U is an f-algebra; the spaces U and V also have some additional structure and are required to satisfy a compatibility condition. Roughly speaking, a V-normed U-module is a module over U that is endowed with a pointwise norm operator taking values in V. The aim of our approach is to develop a unified framework, which is tailored to the differential calculus on metric measure spaces, where as U and V one can take many different spaces of functions.