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

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

Publisher: De Gruyter

: 2024

: Mathematica Slovaca

: 74

: 1

: 143

: 150

: 0139-9918

: 1337-2211

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

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

: https://arxiv.org/pdf/2209.01406(external)

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

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.

:
Oleksiy Dovgoshey was supported by Volkswagen Stiftung Project “From Modeling and Analysis to Approximation”