Displaying similar documents to “On individual subsequential ergodic theorem in von Neumann algebras”

On the (C,α) uniform ergodic theorem

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.

Banach principle in the space of τ-measurable operators

Michael Goldstein, Semyon Litvinov (2000)

Studia Mathematica

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We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.

Operators with an ergodic power

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.

Uniformly ergodic A-contractions on Hilbert spaces

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...

Hopf's ratio ergodic theorem by inducing

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.

On measure theoretical analogues of the Takesaki structure theorem for type III factors

Alexandre Danilenko, Toshihiro Hamachi (2000)

Colloquium Mathematicae

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The orbit equivalence of type I I I 0 ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type I I I 0 cocycles with values in Abelian groups.