Sufficiency and strong commutants in quantum probability theory

DOI10.1007/BF02881073zbMath0635.46058MaRDI QIDQ1097479

Subhash J. Bhatt

Publication date: 1986

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

Heisenberg commutation relationprobability algebrafaithful stateExistence of coarse-grainingHalmos- Savage theoremRadon-Nikodym derivatesunbounded noncommutative probability theory

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Commutators, derivations, elementary operators, etc. (47B47) Applications of selfadjoint operator algebras to physics (46L60) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Miscellaneous applications of functional analysis (46N99)

Cites Work

• Unnamed Item
• Sufficiency and relative entropy in *-algebras with applications in quantum systems
• Conditional expectation in an operator algebra. II
• Sufficiency, KMS condition and relative entropy in von Neumann algebras
• Unbounded representations of \(^*\)-algebras
• Conditional expectations on von Neumann algebras: A new approach
• A Radon-Nikodym theorem for *-algebras
• The free fermion field as a Markov field
• Self-adjoint algebras of unbounded operators
• Conditional expectations in von Neumann algebras
• Non-commutative L^P-spaces
• A Noncommutative Probability Theory
• Noncommutative Probability on von Neumann Algebras
• Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics

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