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### On the Limit of Weighted Operator Averages.

Mathematische Annalen

### On Weak Convergence of Norm Preserving Operators on L2 (X) and its Application to Measure Preserving Transformations.

Mathematische Zeitschrift

### Operators on continuous function spaces and L1-spaces

Colloquium Mathematicae

### Operators on some function spaces

Colloquium Mathematicae

### On invariant measures for power bounded positive operators

Studia Mathematica

We give a counterexample showing that $\overline{\left(I-T*\right){L}_{\infty }}\cap {L}_{\infty }^{+}=0$ does not imply the existence of a strictly positive function u in ${L}_{1}$ with Tu = u, where T is a power bounded positive linear operator on ${L}_{1}$ 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

Studia Mathematica

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 ${n}^{-1}{\sum }_{i=0}^{n-1}f\circ {\tau }^{i}\left(x\right)$ converges almost everywhere to a function f* in $L\left({p}_{1},{q}_{1}\right]$, where (pq) and $\left({p}_{1},{q}_{1}\right]$ are assumed to be in the set $\left(r,s\right):r=s=1,or1. 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

Colloquium Mathematicae

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=(${u}_{1}$, ... ,${u}_{d}\right)$, ${u}_{i}$ ≥ 0, 1 ≤ i ≤ d be a strongly measurable d-parameter semigroup of linear contractions on ${L}_{1}$((Ω,Σ,μ);X). We assume that to each T(u) there corresponds a positive linear contraction P(u) defined on ${L}_{1}$((Ω,Σ,μ);ℝ) with the property that ∥ T(u)f(ω)∥ ≤ P(u)∥f(·)∥(ω) almost everywhere on Ω for all f ∈ ${L}_{1}$((Ω,Σ,μ);X). We then prove stochastic and pointwise ergodic theorems for a d-parameter...

### A general differentiation theorem for superadditive processes

Colloquium Mathematicae

Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T=${T}_{t}$: 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

Colloquium Mathematicae

### On the individual ergodic theorem for subsequences

Studia Mathematica

### On local ergodic theorems for positive semigroups

Studia Mathematica

### A general ratio ergodic theorem for Abel sums

Studia Mathematica

### A mean ergodic theorem for a contraction semigroup in Lebesgue space

Studia Mathematica

### On a local ergodic theorem

Studia Mathematica

### Ratio limit theorems and applications to ergodic theory

Studia Mathematica

### Invariant measures for semigroups

Studia Mathematica

### A reverse maximal ergodic theorem

Studia Mathematica

### Pointwise ergodic theorems for functions in Lorentz spaces ${L}_{pq}$ with p ≠ ∞

Studia Mathematica

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 ${L}_{pq}$ 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 ${L}_{\infty }$

Studia Mathematica

Let $T=T\left(u\right):u\in {ℝ}_{d}^{+}$ be a strongly continuous d-dimensional semigroup of linear contractions on ${L}_{1}\left(\left(\Omega ,\Sigma ,\mu \right);X\right)$, where (Ω,Σ,μ) is a σ-finite measure space and X is a reflexive Banach space. Since ${L}_{1}\left(\left(\Omega ,\Sigma ,\mu \right);X\right)*={L}_{\infty }\left(\left(\Omega ,\Sigma ,\mu \right);X*\right)$, the adjoint semigroup $T*=T*\left(u\right):u\in {ℝ}_{d}^{+}$ becomes a weak*-continuous semigroup of linear contractions acting on ${L}_{\infty }\left(\left(\Omega ,\Sigma ,\mu \right);X*\right)$. In this paper the local ergodic theorem is studied for the adjoint semigroup T*. Assuming that each T(u), $u\in {ℝ}_{d}^{+}$, has a contraction majorant P(u) defined on ${L}_{1}\left(\left(\Omega ,\Sigma ,\mu \right);ℝ\right)$, that is, P(u) is a positive linear contraction on ${L}_{1}\left(\left(\Omega ,\Sigma ,\mu \right);ℝ\right)$ such that $‖T\left(u\right)f\left(\omega \right)‖\le P\left(u\right)‖f\left(·\right)‖\left(\omega \right)$ almost everywhere...

### On the ratio maximal functions for an ergodic flow

Studia Mathematica

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