On a local ergodic theorem
Ryotaro Sato (1976)
Studia Mathematica
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Ryotaro Sato (1976)
Studia Mathematica
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S. McGrath (1981)
Studia Mathematica
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Ryotaro Sato (1980)
Studia Mathematica
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S. McGrath (1977)
Studia Mathematica
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Delio Mugnolo (2004)
Studia Mathematica
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In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space X with a basis. (i) X is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on X is uniformly mean ergodic. (ii) X is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on X is mean ergodic. ...
Takeshi Yoshimoto (1982)
Studia Mathematica
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Ryotaro Sato (1999)
Colloquium Mathematicae
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Let X be a reflexive Banach space and (Ω,Σ,μ) be a σ-finite measure space. Let d ≥ 1 be an integer and T=T(u):u=(, ... ,, ≥ 0, 1 ≤ i ≤ d be a strongly measurable d-parameter semigroup of linear contractions on ((Ω,Σ,μ);X). We assume that to each T(u) there corresponds a positive linear contraction P(u) defined on ((Ω,Σ,μ);ℝ) with the property that ∥ T(u)f(ω)∥ ≤ P(u)∥f(·)∥(ω) almost everywhere on Ω for all f ∈ ((Ω,Σ,μ);X). We then prove stochastic and pointwise ergodic theorems...
Ryotaro Sato (1976)
Studia Mathematica
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Teresa Bermúdez, Manuel González, Mostafa Mbekhta (1998)
Extracta Mathematicae
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Ryotaro Sato (1995)
Publicacions Matemàtiques
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In this paper we give an operator theoretic version of a recent result of F. J. Martín-Reyes and A. de la Torre concerning the problem of finding necessary and sufficient conditions for a nonsingular point transformation to satisfy the Pointwise Ergodic Theorem in Lp. We consider a positive conservative contraction T on L1 of a σ-finite measure space (X, F, μ), a fixed function