On local ergodic theorems for positive semigroups
Ryotaro Sato (1978)
Studia Mathematica
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Ryotaro Sato (1978)
Studia Mathematica
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Ryotaro Sato (1976)
Studia Mathematica
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Ryotaro Sato (1980)
Studia Mathematica
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Paweł Głowacki (1981)
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 (1995)
Studia Mathematica
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Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average converges almost everywhere to a function f* in , where (pq) and are assumed to be in the set . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...
R. Emilion (1985)
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. ...
Teresa Bermúdez, Manuel González, Mostafa Mbekhta (1998)
Extracta Mathematicae
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Takeshi Yoshimoto (1982)
Studia Mathematica
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Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)
Studia Mathematica
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We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.