A generalization of Wigner’s unitary–antiunitary theorem to Hilbert modules

DOI10.1063/1.533044zbMath0953.46030arXivmath/9909049OpenAlexW2053452247MaRDI QIDQ4498473

Lajos Molnár

Publication date: 16 August 2000

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9909049

zbMATH Keywords

Hilbert modulesbijective mappingWigner's unitarity-antiunitarity theorem

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Applications of operator theory in the physical sciences (47N50) (C^*)-modules (46L08) Applications of selfadjoint operator algebras to physics (46L60) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Related Items (11)

Wigner’s theorem in Hilbert $C^*$-modules over $C^*$-algebras of compact operators ⋮ Wigner’s theorem in a class of Hilbert C*-modules ⋮ Tingley's problem for \(p\)-Schatten von Neumann classes ⋮ Maps preserving the \(c\)-numerical radius of products for operators in \(\mathfrak{B}(\mathcal{H})\) ⋮ Perturbation of the Wigner equation in inner product C*-modules ⋮ (No) Wigner Theorem for C*-algebras ⋮ On superstability of the Wigner equation ⋮ Applications of Wigner's theorem to positive maps preserving norm of operator products ⋮ The \(c\)-numerical range of operator products on \({\mathcal{B}}(H)\) ⋮ Representation of symmetry transformations on the sets of tripotents of spin and Cartan factors ⋮ Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem

Cites Work

• Hilbert B(H)-modules and stationary processes
• A direct proof of Wigner's theorem on maps which preserve transition probabilities between pure states of quantum systems
• On Wigner's theorem: Remarks, complements, comments, and corollaries
• A generalized Hilbert space
• Additive isometries on a quaternionic Hilbert space
• The Mackey-Gleason Problem
• Note on Wigner's Theorem on Symmetry Operations

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