The centralizer of ergodic theory group extensions
Jan Kwiatkowski, Mariusz Lemańczyk (1989)
Banach Center Publications
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Jan Kwiatkowski, Mariusz Lemańczyk (1989)
Banach Center Publications
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Sarah Iams, Brian Katz, Cesar E. Silva, Brian Street, Kirsten Wickelgren (2005)
Colloquium Mathematicae
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We study weak mixing and double ergodicity for nonsingular actions of locally compact Polish abelian groups. We show that if T is a nonsingular action of G, then T is weakly mixing if and only if for all cocompact subgroups A of G the action of T restricted to A is weakly mixing. We show that a doubly ergodic nonsingular action is weakly mixing and construct an infinite measure-preserving flow that is weakly mixing but not doubly ergodic. We also construct an infinite measure-preserving...
Isaac Kornfeld, Michael Lin (2000)
Studia Mathematica
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It is well known that a weakly almost periodic operator T in a Banach space is mean ergodic, and in the complex case, also λT is mean ergodic for every |λ|=1. We prove that a positive contraction on is weakly almost periodic if (and only if) it is mean ergodic. An example shows that without positivity the result is false. In order to construct a contraction T on a complex such that λT is mean ergodic whenever |λ|=1, but T is not weakly almost periodic, we prove the following: Let...
Goodson, G.R. (1999)
Acta Mathematica Universitatis Comenianae. New Series
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Day, Sarah L., Grivna, Brian R., McCartney, Earle P., Silva, Cesar E. (1999)
The New York Journal of Mathematics [electronic only]
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Mahesh Nerurkar (2000)
Colloquium Mathematicae
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We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on...
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...
Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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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.
Alexandre I. Danilenko (2010)
Studia Mathematica
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It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly mixing transformation.
A. Al-Hussaini (1974)
Annales Polonici Mathematici
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R. Sato (1990)
Colloquium Mathematicae
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Burgess Davis (1982)
Studia Mathematica
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