The strong law of large numbers for states and traces of aW*-algebra

DOI10.1007/BF01886871zbMath0395.60033OpenAlexW2060916505MaRDI QIDQ4178250

Charles J. K. Batty

Publication date: 1979

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01886871

zbMATH Keywords

Strong Law of Large NumbersW*-Algebra

Mathematics Subject Classification ID

Strong limit theorems (60F15) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (15)

Convergences in \(W^ *\)-algebras ⋮ Exponential convergence rates for weighted sums in noncommutative probability space ⋮ Inequalities for martingales with respect to positive module operators ⋮ Continuity of a quantum stochastic process ⋮ The strong laws of large numbers for positive measurable operators and applications ⋮ Dominated convergence in measure on semifinite von Neumann algebras and arithmetic averages of measurable operators ⋮ Completely positive linear mappings, non-Hamiltonian evolution, and quantum stochastic processes ⋮ Strong Limit Theorems for Orthogonal Sequences in von Neumann Algebras ⋮ Strong laws of large numbers in von Neumann algebras ⋮ Etemadi and Kolmogorov inequalities in noncommutative probability spaces ⋮ Noncommutative Baum--Katz theorems ⋮ A limit in probability in a \(W^*\)-algebra is unique ⋮ Stochastic independence in non-commutative probability theory ⋮ Series of free random variables ⋮ Unbounded derivations tangential to compact groups of automorphisms. II

Cites Work

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• Notes on non-commutative integration
• Zero-one laws in finite \(W^*\)-algebras
• Ergodic theorems for convex sets and operator algebras
• Martingales on von Neumann algebras
• A non-commutative extension of abstract integration
• Convergence in Measure and Related Results in Finite Rings of Operators
• Formes linéaires sur un anneau d'opérateurs

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