Invariant functions for amenable semigroups of positive contractions on $L^{1}$

DOI10.2996/kmj/1138846314zbMath0219.47035OpenAlexW1974906544MaRDI QIDQ5624253

Takahashi, Wataru

Publication date: 1971

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1138846314

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Groups and semigroups of linear operators (47D03)

Related Items (12)

Mean ergodic theorems for semigroups of linear operators ⋮ On the existence of fixed points and ergodic retractions for Lipschitzian semigroups in Hilbert spaces ⋮ Invariant ideals for amenable semigroups of Markov operators ⋮ Mean ergodic theorem for semigroups of linear operators in multi-Banach spaces ⋮ A Nonlinear Ergodic Theorem for an Amenable Semigroup of Nonexpansive Mappings in a Hilbert Space ⋮ Symmetric stable processes on amenable groups ⋮ Ergodic properties of sum- and max-stable stationary random fields via null and positive group actions ⋮ Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: a survey ⋮ On the existence of positive invariant functions for semigroups of operators ⋮ On the existence of invariant functions or Markov representations of amenable semigroups ⋮ Theory of dynamical systems and general transformation groups with invariant measure ⋮ Nonexpansive retractions and nonlinear ergodic theorems in Banach spaces

Cites Work

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• Fixed-point theorems for compact convex sets
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• On existence of finite invariant measures
• On measurable transformations in finite measure spaces
• Proof of the Ergodic Theorem
• Theory of Measure and Invariant Integrals
• Invariant Measures for Markov Processes
• Iterates of Measurable Transformations and Markov Operators
• A Theorem on Amenable Semigroups
• Fixed point theorem for amenable semigroup of nonexpansive mappings
• Invariant ideals for amenable semigroups of Markov operators
• Weakly Wandering Sets and Invariant Measures
• Ergodic theorems and the Markoff process with a stable distribution

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