An Axiomatic Theory Of Normed Modules Via Riesz Spaces
Year: 2024
Type: article
Abstract: ABSTRACT 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 U and V can take many different spaces of functions.
Authors: Danka Lučić, Enrico Pasqualetto
Institution: University of Jyväskylä
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,184
OpenAlex ID: W4404495782