相关论文: Mean ergodicity of multiplication operators in wei…

In this paper, the power boundedness and mean ergodicity of multiplication operators are investigated on the Bloch space B, the little Bloch space B0 and the Besov Space Bp. We completely characterize power bounded, mean ergodic and…

We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…

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…

For operators defined on locally convex spaces we define the notions of boundedness and ergodicity associated to an infinite matrix. Given two matrices $ A$ and $ B$, we study when $ A$-bounded operators are $ B$-ergodic. Using this…

We characterize the geometrically doubling condition of a metric space in terms of the uniform $L^1$-boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.

We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Ces\`aro bounded and strong Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In…

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…

In this article, we characterize the bounded and the compact multiplication operators between distinct iterated logarithmic Lipschitz spaces, and between the Lipschitz space and an iterated logarithmic Lipschitz space of an infinite tree.…

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded…

In this paper, we completely characterize the order boundedness of weighted composition operators between different weighted Dirichlet spaces and different derivative Hardy spaces.

We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…

We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…

Necessary and sufficient conditions are given for mean ergodicity, power boundedness, and topologizability for weighted backward shift and weighted forward shift operators, respectively, on K\"othe echelon spaces in terms of the weight…

We prove that averaging operators are uniformly bounded on $L^1$ for all geometrically doubling metric measure spaces, with bounds independent of the measure. From this result, the $L^1$ convergence of averages as $r \to 0$ immediately…

Let $T$ be a power bounded Hilbert space operator without unimodular eigenvalues. We show that the subsequential ergodic averages $N^{-1}\sum_{n=1}^N T^{a_n}$ converge in the strong operator topology for a wide range of sequences $(a_n)$,…

In this paper the stability and the perturbation bounds of Markov operators acting on abstract state spaces are investigated. Here, an abstract state space is an ordered Banach space where the norm has an additivity property on the cone of…

We present a brief survey of recent results on boundedness of some classical operators within the frameworks of weighted spaces $L^{p(\cdot)}(\varrho)$ with variable exponent $p(x)$, mainly in the Euclidean setting and dwell on a new result…

This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the boundary data belongs to Lebesgue spaces with weights in the…

In this paper, we provide some sufficient conditions for the compactness of weighted composition operators on Dirichlet space. Furthermore, we characterize the numerical range of certain classes of weighted composition operators on…

We introduce a class of iterated logarithmic Lipschitz spaces $\mathcal{L}^{(k)}$, $k\in\mathbb{N}$, on an infinite tree which arise naturally in the context of operator theory. We characterize boundedness and compactness of the…