Related papers: Composition operators on spaces of double Dirichle…
V. Matache (J. Operator Theory 73(1):243--264, 2015) raised an open problem about characterizing composition operators $C_{\phi}$ on the Hardy space $H^2$ and nonzero singular measures $\mu_1$, $\mu_2$ on the unit circle such that…
In this paper, we investigate Li-Yorke composition operators and some of their variations on Lorentz spaces. Further, we also study expansive composition operators on these spaces. The work of the paper is essentially based on the work in…
In \cite{CO-Tp-spaces}, the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space $\mathbb{T}_{p}$ defined on a homogeneous rooted tree. In this article, we give equivalent conditions…
In this paper we investigate the following problem: when a bounded analytic function $\phi$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{\phi^n : n = 0, 1, 2, . . . \}$ is orthogonal in $\mathbb{D}$?, and consider the problem of…
In this paper, we initially study when an anti-linear Toeplitz operator is in the commutant of a composition operator. Primarily, we investigate weighted composition operators $W_{g,\psi}$ commuting with complex symmetric weighted…
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
Motivated by the work of Nazarov and Shapiro on the unit disk, we study asymptotic Toeplitzness of composition operators on the Hardy space of the unit sphere in C^n. We extend some of their results but we also show that new phenomena…
In this paper, we study weighted composition operators on the Fock space. We show that a weighted composition operator is cohyponorma if and only if it is normal. Moreover, we give a complete characterization of closed range weighted…
Let H^2(D) denote the classical Hardy space of the open unit disk D in the complex plane. We obtain descriptions of both the spectrum and essential spectrum of composition operators on H^2(D) whose symbols belong to the class S(2)…
We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…
The notion of decomposable operators acting between distinct $L^p$-direct integrals of Banach spaces is introduced. We show that these operators generalize the composition operator, in sense that a mapping is replaced by a binary relation.…
Let $B_{n}$ be the unit ball in the complex vector space $\mathbb{C}^{n}$, and let $\varphi: B_{n}\rightarrow B_{n}$ be a holomorphic mapping. In this paper, we characterize those symbols $\varphi$ such that composition operators…
We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…
In this paper we use orthonormal basis for the Hardy space $H^{2}(\mathbb{T})$, formed by rational functions, to characterize complex symmetric Toeplitz operators on $H^{2}(\mathbb{T})$. As a result, we get examples of these operators whose…
In this work we propose composition products in the class of complex harmonic functions so that the composition of two such functions is again a complex harmonic function. From here we begin the study of the iterations of the functions of…
In this paper, the boundedness and compactness of the difference of composition-differentiation operators $D_\varphi-D_\psi$ acting from Hardy spaces $H^p$ to weighted Bergman spaces $A^q_\alpha$ are completely characterize for all…
The Dunford property $(C)$ for composition operators on $H^p$-spaces ($1<p<\infty$), as well as for their adjoints, is completely characterized within the class of those induced by linear fractional transformations of the unit disc. As a…
It is well known that on the Hardy space $H^2(\mathbb{D})$ or weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ over the unit disk, the adjoint of a linear fractional composition operator equals the product of a composition operator and two…
In this paper, we study the boundedness, compactness and Schatten class membership of composition operators on the weighted $L^{p}$-space of a tree $L^{p}_{\lambda}(T)$ with $1\leq p <\infty$.
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…