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.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2006-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2006/521425 |
| Summary: | 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. |
|---|---|
| ISSN: | 0972-6802 |