Strong Martingale Convergence of Generalized Conditional Expectations on Von Neumann Algebras

DOI10.2307/1999266zbMath0538.46044OpenAlexW4232103932MaRDI QIDQ3324480

Makoto Tsukada, Fumio Hiai

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999266

zbMATH Keywords

left Hilbert algebrasfaithful normal semifinite weightgeneralized conditional expectationsmartingale Tomita-Takesaki theoryNonabelian K-flows

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Noncommutative dynamical systems (46L55) Hilbert algebras (46K15)

Related Items (6)

On entropy functionals of states of operator algebras ⋮ Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras ⋮ Channel divergences and complexity in algebraic QFT ⋮ Strong Convergence of Martingales in von Neumann Algebras ⋮ The Strong Limit of von Neumann Subalgebras with Conditional Expectations ⋮ Martingale-type convergence of modular automorphism groups on von Neumann algebras

Cites Work

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• On the equivalence of the KMS condition and the variational principle for quantum lattice systems
• Tomita's theory of modular Hilbert algebras and its applications
• Conditional expectations in von Neumann algebras
• Conditional expectation in an operator algebra
• Strong Convergence of Martingales in von Neumann Algebras
• The standard form of von Neumann algebras.
• Martingale convergence in von Neumann algebras

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