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2024

A characterization of inner product spaces via norming vectors

Aubrun, Guillaume, Cavichioli, Mathis

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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.

A characterization of inner product spaces via norming vectors · Around

Built on

On inner products in linear, metric spaces
P. Jordan and J. Von Neumann · 1935
Earlier work this paper cites.
Characterizations of inner product spaces
D. Amir · 1986
Earlier work this paper cites.

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