A characterization of inner product spaces via norming vectors
Functional Analysis
2025-04-30 v2
Abstract
A finite-dimensional normed space is an inner product space if and only if the set of norming vectors of any endomorphism is a linear subspace. This theorem was proved by Sain and Paul for real scalars. In this paper, we give a different proof which also extends to the case of complex scalars.
Keywords
Cite
@article{arxiv.2409.12857,
title = {A characterization of inner product spaces via norming vectors},
author = {Guillaume Aubrun and Mathis Cavichioli},
journal= {arXiv preprint arXiv:2409.12857},
year = {2025}
}
Comments
v2 : modified title, added reference to Sain-Paul ; to appear in Canadian Mathemathical Bulletin