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

DOI10.1006/jfan.2002.3970zbMath1010.46023arXivmath/0209057OpenAlexW2080887062MaRDI QIDQ1865301

Lajos Molnár

Publication date: 26 March 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209057

zbMATH Keywords

symmetry transformationsindefinite inner product spacesidempotents Banach spaces

Mathematics Subject Classification ID

Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Representation theory of linear operators (47A67)

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Cites Work

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• Twistor space, Minkowski space and the conformal group
• Symmetry transformations in indefinite metric spaces. A generalization of Wigner's theorem
• Wigner's theorem on symmetries in indefinite metric spaces
• Gleason's theorem in \(W^*J\)-algebras in spaces with indefinite metric
• Generalization of Wigner's unitary-antiunitary theorem for indefinite inner product spaces
• Additive mappings preserving operators of rank one
• Automorphisms of the poset of skew projections
• Group representations in indefinite metric spaces
• A generalization of Wigner’s unitary–antiunitary theorem to Hilbert modules
• Transformations on the set of all \(n\)-dimensional subspaces of a Hilbert space preserving principal angles

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