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Operators preserving orthogonality are isometries

Published online by Cambridge University Press:  14 November 2011

Alexander Koldobsky
Alexander Koldobsky
Affiliation:
University of Texas at San Antonio, Division of Mathematics, Computer Science, and Statistics, San Antonio, TX 78249, U.S.A
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Synopsis

We prove that every operator preserving orthogonality in a real Banach space is an isometry multiplied by a constant.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 5 , 1993 , pp. 835 - 837
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

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