Strong Convergence of Martingales in von Neumann Algebras

DOI10.2307/2045010zbMath0522.46044OpenAlexW4253196060MaRDI QIDQ3672506

Makoto Tsukada

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/2045010

zbMATH Keywords

conditional expectationfaithful normal semifinite weight on a von Neumann algebrastrong and L1 convergence of martingales

Mathematics Subject Classification ID

Generalizations of martingales (60G48) Free probability and free operator algebras (46L54) General theory of von Neumann algebras (46L10) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51)

Related Items (8)

Strong Martingale Convergence of Generalized Conditional Expectations on Von Neumann Algebras ⋮ A noncommutative Gretsky–Ostroy theorem and its applications ⋮ Non-commutative analogues of weak compactness criteria in symmetric spaces ⋮ Non-homogeneous quantum Markov states and quantum Markov fields ⋮ The Strong Limit of von Neumann Subalgebras with Conditional Expectations ⋮ Martingale-type convergence of modular automorphism groups on von Neumann algebras ⋮ Distributional inequalities for noncommutative martingales ⋮ Optimal estimates for martingale transforms

Cites Work

• Unnamed Item
• Pointwise convergence of martingales in von Neumann algebras
• Conditional expectations in von Neumann algebras and a theorem of Takesaki
• On hyperfinite factors of type III\(_0\) and Krieger's factors
• Conditional expectations in von Neumann algebras
• Conditional expectation in an operator algebra
• Strong Martingale Convergence of Generalized Conditional Expectations on Von Neumann Algebras
• Martingale convergence in von Neumann algebras

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