Characterizations of inner product spaces by orthogonal vectors

Characterizations of inner product spaces by orthogonal vectors

Let X be a real normed space with unit closed ball B. We prove that X is an inner product space if and only if it is true that whenever x, y are points in ?B such that the line through x and y supports 22B then x?y in the sense of Birkhoff.

Bibliographic Details
Main Authors: Marco Baronti, Emanuele Casini
Format: Article
Language:English
Published: Hindawi Limited 2006-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2006/521425
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spelling doaj-1c260b02bd5b4fd2bc8b3047d8ad98af2020-11-24T23:50:05ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022006-01-01411610.1155/2006/521425Characterizations of inner product spaces by orthogonal vectorsMarco Baronti0Emanuele Casini1Dipartimento di Ingegneria della Produzione e Metodi e Modelli Matematici, Università degli studi di Genova, Piazzale Kennedy, Pad. D, 16129 Genova, ItalyDipartimento di Fisica e Matematica, Università dell'Insubria, Via Valleggio 11, 22100 Como, ItalyLet X be a real normed space with unit closed ball B. We prove that X is an inner product space if and only if it is true that whenever x, y are points in ?B such that the line through x and y supports 22B then x?y in the sense of Birkhoff.http://dx.doi.org/10.1155/2006/521425
collection DOAJ
language English
format Article
sources DOAJ
author Marco Baronti
Emanuele Casini
spellingShingle Marco Baronti
Emanuele Casini
Characterizations of inner product spaces by orthogonal vectors
Journal of Function Spaces and Applications
author_facet Marco Baronti
Emanuele Casini
author_sort Marco Baronti
title Characterizations of inner product spaces by orthogonal vectors
title_short Characterizations of inner product spaces by orthogonal vectors
title_full Characterizations of inner product spaces by orthogonal vectors
title_fullStr Characterizations of inner product spaces by orthogonal vectors
title_full_unstemmed Characterizations of inner product spaces by orthogonal vectors
title_sort characterizations of inner product spaces by orthogonal vectors
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
publishDate 2006-01-01
description Let X be a real normed space with unit closed ball B. We prove that X is an inner product space if and only if it is true that whenever x, y are points in ?B such that the line through x and y supports 22B then x?y in the sense of Birkhoff.
url http://dx.doi.org/10.1155/2006/521425
work_keys_str_mv AT marcobaronti characterizationsofinnerproductspacesbyorthogonalvectors
AT emanuelecasini characterizationsofinnerproductspacesbyorthogonalvectors
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