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Ergodic properties of contraction semigroups in L p , 1 < p <

Ryotaro Sato (1994)

Commentationes Mathematicae Universitatis Carolinae

Let { T ( t ) : t > 0 } be a strongly continuous semigroup of linear contractions in L p , 1 < p < , of a σ -finite measure space. In this paper we prove that if there corresponds to each t > 0 a positive linear contraction P ( t ) in L p such that | T ( t ) f | P ( t ) | f | for all f L p , then there exists a strongly continuous semigroup { S ( t ) : t > 0 } of positive linear contractions in L p such that | T ( t ) f | S ( t ) | f | for all t > 0 and f L p . Using this and Akcoglu’s dominated ergodic theorem for positive linear contractions in L p , we also prove multiparameter pointwise ergodic and local ergodic theorems...

Ergodic theorems and perturbations of contraction semigroups

Marta Tyran-Kamińska (2009)

Studia Mathematica

We provide sufficient conditions for sums of two unbounded operators on a Banach space to be (pre-)generators of contraction semigroups. Necessary conditions and applications to positive emigroups on Banach lattices are also presented.

Ergodic theorems in fully symmetric spaces of τ-measurable operators

Vladimir Chilin, Semyon Litvinov (2015)

Studia Mathematica

Junge and Xu (2007), employing the technique of noncommutative interpolation, established a maximal ergodic theorem in noncommutative L p -spaces, 1 < p < ∞, and derived corresponding maximal ergodic inequalities and individual ergodic theorems. In this article, we derive maximal ergodic inequalities in noncommutative L p -spaces directly from the results of Yeadon (1977) and apply them to prove corresponding individual and Besicovitch weighted ergodic theorems. Then we extend these results to noncommutative...

Ergodic transforms associated to general averages

H. Aimar, A. L. Bernardis, F. J. Martín-Reyes (2010)

Studia Mathematica

Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a unified treatment of the ergodic transforms associated to positive groups induced by nonsingular flows and to general means which include the usual averages, Cesàro-α averages and Abel means. We prove the boundedness in L p , 1 < p < ∞, of the maximal ergodic transforms assuming that the semigroup is Cesàro bounded in L p . For p = 1 we find that the maximal ergodic...

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