A characterization of inner product spaces via norming vectors
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866908341531312128 |
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| author | Aubrun, Guillaume Cavichioli, Mathis |
| author_facet | Aubrun, Guillaume Cavichioli, Mathis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of inner product spaces via norming vectors Aubrun, Guillaume Cavichioli, Mathis Functional Analysis 46C15 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. |
| title | A characterization of inner product spaces via norming vectors |
| topic | Functional Analysis 46C15 |
| url | https://arxiv.org/abs/2409.12857 |