Related papers: Approximation numbers of weighted composition oper…
In this paper, we prove that the null space of a weighted composition operator on $\ell_p~ (1 \leq p < \infty)$ is a complemented subspace. We also give a necessary and sufficient condition for a weighted composition operator on $\ell_p$…
This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…
We investigate the norm identity $\|uC_\phi + T\| = \|u\|_\infty + \|T\|$ for classes of operators on $C(S)$, where $S$ is a compact Hausdorff space without isolated point, and characterize those weighted composition operators which satisfy…
It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…
Let $t\in(0,\infty)$, $p\in(1,\infty)$, $q\in[1,\infty]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical…
By establishing some reproducing kernel estimates, we characterize the bounded, compact and Schatten $p$-class Toeplitz operators with positive measure symbols on the weighted Fock space $F^2_{\alpha,w}$ for $p\geq1$, where $w$ is a weight…
In this work, we develop a unified framework for quasidiagonal and F\o lner-type approximations of linear operators on Hilbert spaces. These approximations (originally formulated for bounded operators and operator algebras) involve…
Finite-dimensional model spaces are quotient spaces of the Hardy space on the open unit disc, determined by finite Blaschke products. Composition operators, on the other hand, act by composing Hardy space functions with analytic self-maps…
Let $0<\alpha<n$ and $I_\alpha$ be the fractional integral operator. In this paper, we shall use a unified approach to show some boundedness properties of commutators $[b,I_\alpha]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under…
We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space $H^2$ on the unit disc. This answers a question posed by Shapiro and Sundberg in 1990. We also establish…
In this paper, we characterize bounded, compact and order bounded sum of weighted differentiation composition operators from Bergman type spaces to weighted Banach spaces of analytic functions, where the sum of weighted differentiation…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded…
We study composition 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 and the essential norm. In addition, we study the isometric…
We show that the decay of approximation numbers of compact composition operators on the Dirichlet space $\mathcal{D}$ can be as slow as we wish, which was left open in the cited work. We also prove the optimality of a result of…
The concepts of weighted numerical radius has been defined in recent times. In this article, we obtain several upper bound for weighted numerical radius of operators and $2 \times 2$ operator matrices which generalize and improves some well…
For certain weighted locally convex spaces $X$ and $Y$ of one real variable smooth functions, we characterize the smooth functions $\varphi: \mathbb{R} \to \mathbb{R}$ for which the composition operator $C_\varphi: X \to Y, \, f \mapsto f…
We obtain new lower and upper bounds for the numerical radius of a bounded linear operator $A$ on a complex Hilbert space, which refine the existing ones. In particular, if $w(A)$ and $\|A\|$ denote the numerical radius and operator norm of…
We use induction and interpolation techniques to prove that a composition operator induced by a map $\phi$ is bounded on the weighted Bergman space $\A^2_\alpha(\mathbb{H})$ of the right half-plane if and only if $\phi$ fixes $\infty$…
This paper considers composition operators on Zen spaces (a class of weighted Bergman spaces of the right half-plane related to weighted function spaces on the positive half-line by means of the Laplace transform). Generalizations are given…