Displaying similar documents to “Abelian ergodic theorems for contraction semigroups”

Ergodic theorems and perturbations of contraction semigroups

Marta Tyran-Kamińska (2009)

Studia Mathematica

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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.

On a vector-valued local ergodic theorem in L ∞

Ryotaro Sato (1999)

Studia Mathematica

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Let T = T ( u ) : u ∈ ℝ d + be a strongly continuous d-dimensional semigroup of linear contractions on L 1 ( ( Ω , Σ , μ ) ; X ) , where (Ω,Σ,μ) is a σ-finite measure space and X is a reflexive Banach space. Since L 1 ( ( Ω , Σ , μ ) ; X ) * = L ∞ ( ( Ω , Σ , μ ) ; X * ) , the adjoint semigroup T * = T * ( u ) : u ∈ ℝ d + becomes a weak*-continuous semigroup of linear contractions acting on L ∞ ( ( Ω , Σ , μ ) ; X * ) . In this paper the local ergodic theorem is studied for the adjoint semigroup T*. Assuming that each T(u), u ∈ ℝ d + , has a contraction majorant P(u) defined on L 1 ( ( Ω , Σ , μ ) ; ℝ ) , that is, P(u) is a positive linear contraction on L 1 ( ( Ω , Σ , μ ) ; ℝ ) such that ‖ T ( u ) f ( ω ) ‖ ≤ P ( u ) ‖ f ( · ) ‖ ( ω ) almost...

A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis

Delio Mugnolo (2004)

Studia Mathematica

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In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space X with a basis. (i) X is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on X is uniformly mean ergodic. (ii) X is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on X is mean ergodic. ...

A -systems

R. Gorton (1976)

Compositio Mathematica

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