On functions with scattered spectra on lea groups
Paweł Głowacki (1981)
Studia Mathematica
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Paweł Głowacki (1981)
Studia Mathematica
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Charles Pugh, Michael Shub (1971)
Compositio Mathematica
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Alexandre Danilenko, Toshihiro Hamachi (2000)
Colloquium Mathematicae
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The orbit equivalence of type 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 cocycles with values in Abelian groups.
J. Choksi, M. Nadkarni (2000)
Colloquium Mathematicae
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It is shown that in the group of invertible measurable nonsingular transformations on a Lebesgue probability space, endowed with the coarse topology, the transformations with infinite ergodic index are generic; they actually form a dense set. (A transformation has infinite ergodic index if all its finite Cartesian powers are ergodic.) This answers a question asked by C. Silva. A similar result was proved by U. Sachdeva in 1971, for the group of transformations preserving an infinite...
Alexandre Danilenko (2000)
Colloquium Mathematicae
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We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
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...
Alexandre Danilenko, Mariusz Lemańczyk (1999)
Studia Mathematica
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We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension and admits a prescribed subgroup in the centralizer of .
Ryotaro Sato (1980)
Studia Mathematica
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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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...
H. B. Keynes, D. Newton (1976)
Compositio Mathematica
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