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arXiv:math/0209057 [math.FA]AbstractReferencesReviewsResources

Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem

Lajos Molnar

Published 2002-09-06Version 1

We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents of a Banach space which preserve zero products in both directions.

Comments: 13 pages, To appear in J. Funct. Anal
Categories: math.FA, quant-ph
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