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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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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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...
J. Woś (1987)
Colloquium Mathematicae
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Janusz Woś (1987)
Colloquium Mathematicae
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J. Michael Steele (1989)
Annales de l'I.H.P. Probabilités et statistiques
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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.
Elmouloudi Ed-dari (2003)
Studia Mathematica
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We improve a recent result of T. Yoshimoto about the uniform ergodic theorem with Cesàro means of order α. We give a necessary and sufficient condition for the (C,α) uniform ergodicity with α > 0.
R. Sato (1990)
Colloquium Mathematicae
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Paweł Głowacki (1981)
Studia Mathematica
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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...
Charles Pugh, Michael Shub (1971)
Compositio Mathematica
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