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Orthogonality and characterizations of inner product spaces

Published online by Cambridge University Press:  17 April 2009

O.P. Kapoor  and
Jagadish Prasad
O.P. Kapoor
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India.
Jagadish Prasad
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India.
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Abstract

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Using the notions of orthogonality in normed linear spaces such as isosceles, pythagorean, and Birkhoff-James orthogonality, in this paper we provide some new characterizations of inner product spaces besides giving simpler proofs of existing similar characterizations. In addition we prove that in a normed linear space pythagorean orthogonality is unique and that isosceles orthogonality is unique if and only if the space is strictly convex.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 3 , December 1978 , pp. 403 - 416
Copyright
Copyright © Australian Mathematical Society 1979

References

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