Strong limit theorems in noncommutative \(L_ 2\)-spaces

DOI10.1007/BFb0098424zbMath0743.46069MaRDI QIDQ1188986

Ryszard Jajte

Publication date: 18 September 1992

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

ergodic theoremsalmost everywhere convergence\(\sigma\)-finite von Neumann algebra with a faithful normal statenon-commutative version of a theorem of Burkholder and Chow on the convergence of the iterates of two conditional expectationnon-commutative version of a theorem of E. Stein on the convergence of the iterates of a positive contraction in \(L^ 2\)non-commutative versions of pointwise convergence theorems in \(L^ 2\)- spacesNon-commutative versions of the Rademacher-Menshov theorem for series of orthogonal functions and of the martingale convergen

Mathematics Subject Classification ID

Strong limit theorems (60F15) Ergodic theory of linear operators (47A35) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02)

Related Items (14)

Individual ergodic theorem for unitary maps of random matrices ⋮ Noncommutative Burkholder/Rosenthal inequalities ⋮ Quantitative mean ergodic inequalities: power bounded operators acting on one single noncommutative \(L_p\) space ⋮ Dominated convergence theorems in Haagerup noncommutative \(L_p\)-spaces ⋮ On multiparameter weighted ergodic theorem for noncommutative \(L_p\)-spaces ⋮ Maximal theorems of Menchoff--Rademacher type in non-commutative \(L_{q}\)-spaces. ⋮ Noncommutative strong maximals and almost uniform convergence in several directions ⋮ A reduction method for noncommutative 𝐿_{𝑝}-spaces and applications ⋮ Noncommutative extrapolation theorems and applications ⋮ The classical monotone convergence theorem of Beppo Levi fails in noncommutative $L_2$-spaces ⋮ On ergodic theorems for free group actions on noncommutative spaces ⋮ Noncommutative Baum--Katz theorems ⋮ Noncommutative maximal ergodic theorems ⋮ Bundle convergence of harmonic means of orthogonal sequences in noncommutative \(L_2\)-spaces

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