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On maps that preserve orthogonality in normed spaces

Published online by Cambridge University Press:  12 July 2007

A. Blanco  and
A. Turnšek
A. Blanco
Affiliation:
Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, UK ([email protected])
A. Turnšek
Affiliation:
Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, 1000 Ljubljana, Slovenia ([email protected])
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Abstract

We show that every orthogonality-preserving linear map between normed spaces is a scalar multiple of an isometry. Using this result, we generalize Uhlhorn's version of Wigner's theorem on symmetry transformations to a wide class of Banach spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 4 , August 2006 , pp. 709 - 716
Copyright
Copyright © Royal Society of Edinburgh 2006

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