On Quasi-Invariant Measures in Uniquely Ergodic Systems.
Wolfgang Krieger (1971)
Inventiones mathematicae
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Wolfgang Krieger (1971)
Inventiones mathematicae
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Jon Aaronson (1977)
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Donald S. Ornstein (1975)
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Journal of Convex Analysis
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Laurian Suciu (2009)
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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...
Wojciech Bartoszek (1987)
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Jon Aaronson, Tom Meyerovitch (2008)
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We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.
Alexander I. Bufetov (2014)
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The main result of this note, Theorem 1.3, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant and ergodic under the action of the infinite unitary group and that admits well-defined projections onto the quotient space of “corners" of finite size, must be finite. A similar result, Theorem 1.1, is also established for unitarily invariant measures on the space of all infinite complex matrices. These results imply that the infinite Hua-Pickrell...
Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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Janusz Woś (1987)
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Roland Zweimüller (2004)
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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.
J. Woś (1987)
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S. Doplicher, D. Kastler (1968)
Recherche Coopérative sur Programme n°25
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R. Sato (1990)
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Basic ergodic properties of the ELF class of automorphisms, i.e. of the class of ergodic automorphisms whose weak closure of measures supported on the graphs of iterates of T consists of ergodic self-joinings are investigated. Disjointness of the ELF class with: 2-fold simple automorphisms, interval exchange transformations given by a special type permutations and time-one maps of measurable flows is discussed. All ergodic Poisson suspension automorphisms as well as dynamical systems...
Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)
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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.