Related papers: Dynamics on weighted solid Banach function spaces
A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports…
In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of…
We study inclusion relations between Gelfand-Shilov type spaces defined via a weight (multi-)sequence system, a weight function system, and a translation-invariant Banach function space. We characterize when such spaces are included into…
A kind of generalized Gelfand pair is introduced via a Banach algebra consisting of bi-invariant functions in a weighted Lebesgue space. The related spherical functions and the Fourier transformation are constructed. The multipliers of the…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…
In this note we study sub-Hardy Hilbert spaces on which the the action of the operator of multiplication by the coordinate function z is assumed to be weaker than that of an isometry. We identify such operators with a class of weighted…
We use properties of the sequences of zeros of certain spaces of analytic functions in the unit disc $\mathbb D$ to study the question of characterizing the weighted superposition operators which map one of these spaces into another. We…
In this paper, we study distributional chaos for weighted translations on locally compact groups. We give a sufficient condition for such operators to be distributionally chaotic and construct an example of distributionally chaotic weighted…
We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$.
This paper discusses the properties of a modified version of the Stancu variant Sz\'asz-Mirakjan Kantorovich type operators. We determine the order of approximation in terms of the modulus of continuity and second-order of smoothness, and…
We study the dynamic behaviour of (weighted) composition operators on the space of holomorphic functions on a plane domain. Any such operator is hypercyclic if and only if it is topologically mixing, and when the symbol is automorphic, such…
The boundedness and compactness of weighted composition operators from $H^\infty$ to the Bloch space in the unit ball of Cn are investigated in this paper. In particular, some new characterizations for the boundedness and the essential norm…
In this paper, we characterize the boundedness and the compactness of weighted composition operators acting on a de Branges-Rovnyak space $\mathcal H(b)$, where the symbol $b$ is a rational function in the unit ball of $H^\infty$ that is…
We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite…
We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on Banach spaces of sequences on Z and the spectrum of operators commuting with the shift on Banach spaces of sequences on Z^+.We generalize the…
In the early 1970's Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity, supercyclicity,…
Using recent characterizations of the compactness of composition operators on Hardy-Orlicz and Bergman-Orlicz spaces on the ball, we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has…
The existence of the Oseledets decomposition on continuously embedded subspaces of Banach spaces is proved in this paper. Natural assumptions facilitating such transfer of the Oseledets decomposition are presented, notably conditions often…
The purpose of the present work is to treat a new notion related to linear dynamics, which can be viewed as a "localization" of the notion of hypercyclicity. In particular, let $T$ be a bounded linear operator acting on a Banach space $X$…
We consider analytic coupled map lattices over $\Z^d$ with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures with analytic, exponentially bounded finite dimensional…