Geodesic
A characterization of inner product spaces via norming vectors
Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 598-602

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DOI

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.
DOI : 10.4153/S0008439524000985
Mots-clés : Characterization of inner-product spaces, norming vectors, positive John position 
Aubrun, Guillaume; Cavichioli, Mathis. A characterization of inner product spaces via norming vectors. Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 598-602. doi: 10.4153/S0008439524000985
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     title = {A characterization of inner product spaces via norming vectors},
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     year = {2025},
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     doi = {10.4153/S0008439524000985},
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