Some Open Problems in Ergodic Theory
Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Roger Jones (1980)
Studia Mathematica
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Laurian Suciu (2009)
Studia Mathematica
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We study the concept of uniform (quasi-) A-ergodicity for A-contractions on a Hilbert space, where A is a positive operator. More precisely, we investigate the role of closedness of certain ranges in the uniformly ergodic behavior of A-contractions. We use some known results of M. Lin, M. Mbekhta and J. Zemánek, and S. Grabiner and J. Zemánek, concerning the uniform convergence of the Cesàro means of an operator, to obtain similar versions for A-contractions. Thus, we continue the study...
Janusz Woś (1987)
Colloquium Mathematicae
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Lasha Ephremidze (2003)
Studia Mathematica
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The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized to the ergodic Hilbert transform.
Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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Karl Petersen, Shizuo Kakutani (1981)
Monatshefte für Mathematik
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Roland Zweimüller (2004)
Colloquium Mathematicae
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We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.
Burgess Davis (1982)
Studia Mathematica
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R. Sato (1990)
Colloquium Mathematicae
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Yves Derriennic (2010)
Colloquium Mathematicae
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The aim of this short note is to present in terse style the meaning and consequences of the "filling scheme" approach for a probability measure preserving transformation. A cohomological equation encapsulates the argument. We complete and simplify Woś' study (1986) of the reversibility of the ergodic limits when integrability is not assumed. We give short and unified proofs of well known results about the behaviour of ergodic averages, like Kesten's lemma (1975). The strikingly simple...
Daniel W. Stroock (2010)
Colloquium Mathematicae
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Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves. ...
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.
S. Doplicher, D. Kastler (1968)
Recherche Coopérative sur Programme n°25
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Paweł Głowacki (1981)
Studia Mathematica
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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...
Lasha Ephremidze (2002)
Fundamenta Mathematicae
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It is proved that the ergodic maximal operator is one-to-one.