Banach principle in the space of τ-measurable operators

Michael Goldstein; Semyon Litvinov

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On individual subsequential ergodic theorem in von Neumann algebras

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We use a non-commutative generalization of the Banach Principle to show that the classical individual ergodic theorem for subsequences generated by means of uniform sequences can be extended to the von Neumann algebra setting.

Pointwise Convergence Theorems in L2 over a von Neumann Algebra.

Eva Hensz, Ryszard Jajte (1986)

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Multiparameter pointwise ergodic theorems for Markov operators on L.

Ryotaro Sato (1994)

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Let P₁, ..., P_d be commuting Markov operators on L_∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each P_i is either conservative or invertible, we prove that for every f in L_p(X,F,μ) with 1 ≤ p < ∞ the averages A_nf = (n + 1)^-d Σ_{0≤n_i≤n} P₁