✦ LIBER ✦
Orthogonality Preserving Transformations on Indefinite Inner Product Spaces: Generalization of Uhlhorn's Version of Wigner's Theorem
✍ Scribed by Lajos Molnár
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 146 KB
- Volume
- 194
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
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 rankone idempotents of a Banach space which preserve zero products in both directions.