Related papers: On ergodic operator means in Banach spaces
Recent results concerning the linear dynamics and mean ergodicity of compact operators in Banach spaces, together with additional new results, are employed to investigate various spectral properties of generalized Ces\`aro operators acting…
We use techniques of proof mining to obtain a computable and uniform rate of metastability (in the sense of Tao) for the mean ergodic theorem for a finite number of commuting linear contractive operators on a uniformly convex Banach space.
Classical Banach principle is an essential tool for the investigation of the ergodic properties of Cesaro subsequences. The aim of this work is to extend Banach principle to the case of the stochastic convergence in the operator algebras.…
We extend the classical mean ergodic theorem to the setting of norming dual pairs. It turns out that, in general, not all equivalences from the Banach space setting remain valid in our situation. However, for Markovian semigroups on the…
The semi-invertible version of Oseledets' multiplicative ergodic theorem providing a decomposition of the underlying state space of a random linear dynamical system into fast and slow spaces is deduced for a strongly measurable cocycle on a…
Various properties of the (continuous) Ces\`aro operator $\mathsf{C}$, acting on Banach and Fr\'echet spaces of continuous functions and $L^p$-spaces, are investigated. For instance, the spectrum and point spectrum of $\mathsf{C}$ are…
We study mean ergodic composition operators on infinite dimensional spaces of holomorphic functions of different types when defined on the unit ball of a Banach or a Hilbert space: that of all holomorphic functions, that of holomorphic…
We study strictly ergodic Delone dynamical systems and prove an ergodic theorem for Banach space valued functions on the associated set of pattern classes. As an application, we prove existence of the integrated density of states in the…
For a Dunford-Schwartz operator in the $L^p-$space, $1\leq p< \infty$ , of an arbitrary measure space, we prove pointwise convergence of the conventional and Besicovitch weighted ergodic averages. Pointwise convergence of various types of…
We provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of T. Tao of the Mean Ergodic Theorem for such spaces and so…
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded…
We investigate uniform ergodic type theorems for additive and subadditive functions on a subshift over a finite alphabet. We show that every strictly ergodic subshift admits a uniform ergodic theorem for Banach-space-valued additive…
It is known that Dobrushin's ergodicity coefficient is one of the effective tools in the investigations of limiting behavior of Markov processes. Several interesting properties of the ergodicity coefficient of a positive mapping defined on…
A volume growth-based proof of the Multiplicative Ergodic Theorem for Banach spaces is presented, following the approach of Ruelle for cocycles acting on a Hilbert space. As a consequence, we obtain a volume growth interpretation for the…
We investigate frequently hypercyclic and chaotic linear operators from a measure-theoretic point of view. Among other things, we show that any frequently hypercyclic operator T acting on a reflexive Banach space admits an invariant…
We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with a separable dual.
For a Dunford-Schwartz operator in a fully symmetric space of measurable functions of an arbitrary measure space, we prove pointwise convergence of the conventional and weighted ergodic averages.
In the present paper, we consider random invariant densities and the mean ergodic theorem for Markov operator cocycles which are applicable to quenched type random dynamical systems. We give necessary and sufficient conditions for the…
The Cesaro operator $\mathsf{C}$, when acting in the classical growth Banach spaces $A^{-\gamma}$ and $A_0^{-\gamma}$, for $\gamma > 0 $, of analytic functions on $\mathbb{D}$, is investigated. Based on a detailed knowledge of their spectra…
In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach…