Probability measures in 𝑊*𝐽-algebras in Hilbert spaces with conjugation

DOI10.1090/S0002-9939-98-04176-8zbMath0891.46036MaRDI QIDQ4383106

Marjan Matvejchuk

Publication date: 24 March 1998

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

von Neumann algebraprobability measurequantum logics\(W^*\)-algebra\(J\)-orthogonal projections\(J\)-real bounded operatorscentral summand of type \(I_ 2\)normal finite trace

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Probabilistic methods in Banach space theory (46B09) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Measures on Boolean rings, measure algebras (28A60) Quantum logic (03G12)

Related Items (7)

Unnamed Item ⋮ Idempotents in a space with conjugation ⋮ Idempotents as \(J\)-projections. II ⋮ Any regular measure on conjugation logic is a complex measure ⋮ Von Neumann \(J\) -algebras in a space with two symmetries ⋮ On classification of von Neumann algebras in a space with conjugation ⋮ Von Neumann algebras and projections in space with conjugation operator

Cites Work

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• Measures on the quantum logic of subspaces of a \(J\)-space
• Semiconstant measures on hyperbolic logics

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