Decomposition in direct sum of seminormed vector spaces and Mazur-Ulam theorem - UTU Research Portal

A1 Refereed original research article in a scientific journal

Decomposition in direct sum of seminormed vector spaces and Mazur-Ulam theorem

Authors: Dovgoshey, Oleksiy; Prestin, Jürgen; Shevchuk, Igor

Publisher: De Gruyter

Publication year: 2024

Journal: Mathematica Slovaca

Journal name in source: Mathematica Slovaca

Volume: 74

Issue: 1

First page : 143

Last page: 150

ISSN: 0139-9918

eISSN: 1337-2211

DOI: https://doi.org/10.1515/ms-2024-0010(external)

Web address : https://doi.org/10.1515/ms-2024-0010(external)

Self-archived copy’s web address: https://arxiv.org/pdf/2209.01406(external)

Preprint address: https://arxiv.org/abs/2209.01406(external)

Abstract

It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur–Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.

Funding information in the publication:
Oleksiy Dovgoshey was supported by Volkswagen Stiftung Project “From Modeling and Analysis to Approximation”