On the Limit of Weighted Operator Averages.
On Weak Convergence of Norm Preserving Operators on L2 (X) and its Application to Measure Preserving Transformations.
Operators on continuous function spaces and L1-spaces
Operators on some function spaces
On invariant measures for power bounded positive operators
We give a counterexample showing that does not imply the existence of a strictly positive function u in with Tu = u, where T is a power bounded positive linear operator on of a σ-finite measure space. This settles a conjecture by Brunel, Horowitz, and Lin.
Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations
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 and unified...
Vector-valued ergodic theorems for multiparameter additive processes
Let X be a reflexive Banach space and (Ω,Σ,μ) be a σ-finite measure space. Let d ≥ 1 be an integer and T=T(u):u=(, ... ,, ≥ 0, 1 ≤ i ≤ d be a strongly measurable d-parameter semigroup of linear contractions on ((Ω,Σ,μ);X). We assume that to each T(u) there corresponds a positive linear contraction P(u) defined on ((Ω,Σ,μ);ℝ) with the property that ∥ T(u)f(ω)∥ ≤ P(u)∥f(·)∥(ω) almost everywhere on Ω for all f ∈ ((Ω,Σ,μ);X). We then prove stochastic and pointwise ergodic theorems for a d-parameter...
A general differentiation theorem for superadditive processes
Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T=: t < 0 be a strongly continuous semigroup of positive linear operators on the Banach lattice L. Under some suitable norm conditions on L we prove a general differentiation theorem for superadditive processes in L with respect to the semigroup T.
A note on the almost everywhere convergence of alternating sequences with Dunford-Schwartz operators
On the individual ergodic theorem for subsequences
On local ergodic theorems for positive semigroups
A general ratio ergodic theorem for Abel sums
A mean ergodic theorem for a contraction semigroup in Lebesgue space
On a local ergodic theorem
Ratio limit theorems and applications to ergodic theory
Invariant measures for semigroups
A reverse maximal ergodic theorem
Pointwise ergodic theorems for functions in Lorentz spaces with p ≠ ∞
Let τ be a null preserving point transformation on a finite measure space. Assuming τ is invertible, P. Ortega Salvador has recently obtained sufficient conditions for the almost everywhere convergence of the ergodic averages in with 1 < p < ∞, 1 < q < ∞. In this paper we obtain necessary and sufficient conditions for the almost everywhere convergence, without assuming that τ is invertible and only assuming that p ≠ ∞.
On a vector-valued local ergodic theorem in
Let be a strongly continuous d-dimensional semigroup of linear contractions on , where (Ω,Σ,μ) is a σ-finite measure space and X is a reflexive Banach space. Since , the adjoint semigroup becomes a weak*-continuous semigroup of linear contractions acting on . In this paper the local ergodic theorem is studied for the adjoint semigroup T*. Assuming that each T(u), , has a contraction majorant P(u) defined on , that is, P(u) is a positive linear contraction on such that almost everywhere...
On the ratio maximal functions for an ergodic flow
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