A1 Journal article (refereed)
An Axiomatic Theory Of Normed Modules Via Riesz Spaces (2024)

Lučić, D., & Pasqualetto, E. (2024). An Axiomatic Theory Of Normed Modules Via Riesz Spaces. Quarterly Journal of Mathematics, Early online. https://doi.org/10.1093/qmath/haae053

JYU authors or editors

Publication details

All authors or editors: Lučić, Danka; Pasqualetto, Enrico

Journal or series: Quarterly Journal of Mathematics

ISSN: 0033-5606

eISSN: 1464-3847

Publication year: 2024

Publication date: 19/11/2024

Volume: Early online

Publisher: Oxford University Press

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1093/qmath/haae053

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/98655

Web address of parallel published publication (pre-print):  https://doi.org/10.48550/arXiv.2306.12238

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.

Keywords: functional analysis; differential geometry; metric spaces; modules (mathematics)

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2024

Preliminary JUFO rating: 1