Related papers: Mean ergodic properties of the continuous Ces\`aro…
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…
A detailed investigation is made of the continuity, spectrum and mean ergodic properties of the Ces\`aro operator $C$ when acting on the strong duals of power series spaces of infinite type. There is a dramatic difference in the nature of…
The generalized Ces\`aro operators $C_t$, for $t\in [0,1]$, were first investigated in the 1980's. They act continuously in many classical Banach sequence spaces contained in $\mathbb{C}^{\mathbb{N}_0}$, such as $\ell^p$, $c_0$, $c$,…
An investigation is made of the generalized Ces\`aro operators $C_t$, for $t\in [0,1]$, when they act on the space $H(\mathbb{D})$ of holomorphic functions on the open unit disc $\mathbb{D}$, on the Banach space $H^\infty$ of bounded…
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…
The spectrum of the Ces\`aro operator $\mathsf{C}$ is determined on the spaces which arises as intersections $A^p_{\alpha +}$ (resp. unions $A^p_{\alpha -}$) of Bergman spaces $A_\alpha^p$ of order $1<p<\infty$ induced by standard radial…
Continuity, compactness, the spectrum and ergodic properties of Ces\`aro operators are investigated when they act on the space $VH(\mathbb{D})$ of analytic functions with logarithmic growth on the open unit disc $\mathbb{D}$ of the complex…
Given a symbol $\varphi,$ i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator $C_{\varphi}(f)=f\circ\varphi$ defined on the Banach spaces of holomorphic functions $A(\mathbb{D})$ and…
Unlike for $\ell_p$, $1<p\leq\infty$, the discrete Ces\`aro operator $C$ does not map $\ell_1$ into itself. We identify precisely those weights $w$ such that $C$ does map $\ell_1(w)$ continuously into itself. For these weights a complete…
The discrete Ces\`aro operator $ C $ acts continuously in various classical Banach sequence spaces within $ \mathbb{C}^{\mathbb{N}}.$ For the coordinatewise order, many such sequence spaces $ X $ are also complex Banach lattices (eg. $c_0,…
We describe holomorphic functions and fractional powers of Ces\'{a}ro operators in $L^2(\mathbb{R})$, $L^2(\mathbb{R}_+)$, and $L^2[0,1]$. Logarithms of Ces\'{a}ro operators are introduced as well and their spectral properties are studied.…
Generalized Ces\`aro operators $C_t$, for $t\in [0,1)$, are investigated when they act on the disc algebra $A(\mathbb{D})$ and on the Hardy spaces $H^p$, for $1\leq p \leq \infty$. We study the continuity, compactness, spectrum and point…
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 consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods…
We investigate (uniform) mean ergodicity of weighted composition operators on the space of smooth functions and the space of distributions, both over an open subset of the real line. Among other things, we prove that a composition operator…
In this paper, for $p>1$ and $s>1$, we give a complete description of the boundedness and compactness of a Ces\`aro-like operator from the Besov space $B_p$ into a Banach space $X$ between the mean Lipschitz space $\Lambda^s_{1/s}$ and the…
The discrete Ces\`aro operator $\mathsf{C}$ is investigated in the class of smooth sequence spaces $\lambda_0(A)$ of finite type. This class contains properly the power series spaces of finite type. Of main interest is its spectrum, which…
We completely characterize the mean ergodic composition operators on $H^\infty(\mathbb{B}_n)$. In particular, we show that a composition operator acting on this space is mean ergodic if and only if it is uniformly mean ergodic.
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.
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…