Displaying similar documents to “On heredity of strongly proximal actions”

Strong continuity of invariant probability charges

Harald Luschgy, Sławomir Solecki (2004)

Colloquium Mathematicae

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Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0,1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.

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...