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

2002/09/06 by Lajos Molnár, Lajos Molnar, Molnar, Lajos · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Functional Equations Stability Results #Matrix Theory and Algorithms #Quantum Physics (quant-ph) #math.FA #quant-ph

paper · pdf · doi:10.48550/arxiv.math/0209057

13 pages, To appear in J. Funct. Anal

arxiv created 2002/09/06 · openalex publication_date 2002/09/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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