Symmetries of C ∗-algebras and Jordan Morphisms

DOI10.1007/978-3-031-02104-6_20OpenAlexW4302393828MaRDI QIDQ5888411

Jan Hamhalter, Ekaterina Turilova

Publication date: 25 April 2023

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-02104-6_20

zbMATH Keywords

\(C^\ast \)-algebrasJordan \(^\ast \)-morphisms

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Linear operator inequalities (47A63) Geometry and structure of normed linear spaces (46B20) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Cites Work

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• Active lattices determine \(\mathrm{AW}^\ast\)-algebras
• Dye's theorem and Gleason's theorem for \(AW^\ast\)-algebras
• Automorphisms of order structures of abelian parts of operator algebras and their role in quantum theory
• Orthogonal measures on state spaces and context structure of quantum theory
• Foundations of quantum theory. From classical concepts to operator algebras
• Choquet order and Jordan maps
• Jordan invariants of von Neumann algebras given by abelian subalgebras and Choquet order on state spaces
• Isomorphisms of ordered structures of Abelian \(C^*\)-subalgebras of \(C^*\)-algebras
• On the geometry of projections in certain operator algebras
• Abelian subalgebras and the Jordan structure of a von Neumann algebra
• Linear algebraic proof of Wigner theorem and its consequences
• Quantum measure theory
• Comment on: ``Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

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