Gleason's theorem and completeness of inner product spaces

DOI10.1007/BF00669390zbMath0663.46060MaRDI QIDQ1114131

Ladislav jun. Mišík, Anatolij Dvurečenskij

Publication date: 1988

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

zbMATH Keywords

inner product spaceGleason's theoremcompletely additive statelattice of all strongly closed subspaces

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items (7)

Gleason's theorem and completeness criteria ⋮ State on splitting subspaces and completeness of inner product spaces ⋮ States on families of subspaces of pre-Hilbert spaces ⋮ A signed measure completeness criterion ⋮ Bibliography on quantum logics and related structures ⋮ Quantum logics and completeness criteria of inner product spaces ⋮ Regular measures and inner product spaces

Cites Work

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• Converse of the Eilers-Horst theorem
• The theorem of Gleason for non-separable Hilbert spaces
• Generalization of Maeda's theorem
• A Completeness Criterion for Inner Product Spaces
• Correction to: "Inner Product Spaces"
• Inner Product Spaces
• A remark on Piron's paper
• Partial Solution to Mackey's Problem about Modular Pairs and Completeness
• Generalization of Gleason's theorem

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