Ergodic theorems for noncommutative dynamical systems

DOI10.1007/BF01390100zbMath0374.46058OpenAlexW2027697735MaRDI QIDQ1245414

Nghiem Dang-Ngoc, Jean-Pierre Conze

Publication date: 1978

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142549

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory of linear operators (47A35) General theory of von Neumann algebras (46L10) General theory of locally convex spaces (46A03)

Related Items

McMillan type convergence for quantum Gibbs states ⋮ Ergodic type theorems for finite von Neumann algebras ⋮ Noncommutative multi-parameter Wiener-Wintner type ergodic theorem ⋮ Noncommutative maximal ergodic inequalities associated with doubling conditions ⋮ Quantitative mean ergodic inequalities: power bounded operators acting on one single noncommutative \(L_p\) space ⋮ Local ergodic theorems in symmetric spaces of measurable operators ⋮ Pointwise convergence of martingales in von Neumann algebras ⋮ Maximal ergodic inequalities for some positive operators on noncommutative Lp$L_p$‐spaces ⋮ A reduction method for noncommutative 𝐿_{𝑝}-spaces and applications ⋮ Almost sure convergence theorems in von Neumann algebras ⋮ On noncommutative weighted local ergodic theorems on \(L^p\)-spaces ⋮ Completely positive linear mappings, non-Hamiltonian evolution, and quantum stochastic processes ⋮ On ergodic theorems for free group actions on noncommutative spaces ⋮ On the \(K\)-theory of some \(C^*\)-algebras of Toeplitz and singular integral operators ⋮ Noncommutative maximal ergodic theorems ⋮ On the non-commutative Neveu decomposition and ergodic theorems for amenable group action ⋮ Maximal ergodic theorems in non-commutative \(L_p\)-spaces

Cites Work

• Ergodic theorems for convex sets and operator algebras
• Group structure and the pointwise ergodic theorem for connected amenable groups
• Sur la classification des systèmes dynamiques non commutatifs
• Non-commutative extension of Lusin's theorem
• Invariant states and asymptotic abelianness
• General ergodic theorems
• The Pointwise Ergodic Theorem for Amenable Groups
• Operator Algebras with Weakly Closed Abelian Subalgebras
• Abstract Ergodic Theorems and Weak Almost Periodic Functions
• A general ergodic theorem
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