Pointwise convergence theorems in \(L_ 2\) over a von Neumann algebra

DOI10.1007/BF01229809zbMath0613.46056MaRDI QIDQ1819330

Ryszard Jajte, E. Hensz-Chądzyńska

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173797

zbMATH Keywords

Cesàro meansalmost sure convergencealmost everywhere convergenceergodic Hilbert transformvon Neumann algebra with a faithful normal stateindividual ergodic theorem for unitary operatorsnon- commutative extension of the Rademacher-Menshov theorem

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Strong limit theorems (60F15) Free probability and free operator algebras (46L54) Noncommutative dynamical systems (46L55) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items

A noncommutative generalisation of a problem of Steinhaus ⋮ Almost sure convergence of iterates of contractions in noncommutative \(L_ 2\)-spaces

Cites Work

• Strong limit theorems in non-commutative probability
• Pointwise convergence of martingales in von Neumann algebras
• Ergodic theorems for convex sets and operator algebras
• Pointwise convergence theorems for self-adjoint and unitary contractions
• A non-commutative individual ergodic theorem
• Quasi-Uniform Ergodic Theorems in von Neumann Algebras
• Another Proof of the Existence of the Ergodic Hilbert Transform
• Ergodic theorems for semifinite von Neumann algebras: II
• SOME PROBLEMS OF NON-COMMUTATIVE ERGODIC THEORY
• Ergodic Theorems for Semifinite Von Neumann Algebras-I
• Martingale convergence in von Neumann algebras
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