Weighted Composition Operators Research Articles

Complex symmetric Toeplitz operators on the unit polydisk

In this paper, we study the complex symmetry of Toeplitz operators on the weighted Bergman spaces over the unit polydisk. First, we completely characterize when anti-linear weighted composition operators [Formula: see text] are conjugations. We then give a sufficient and necessary condition for Toeplitz operators to be complex symmetric with respect to these conjugations. As a consequence, some interesting higher-dimensional complex symmetric phenomena appear on the unit polydisk such as the monomial Toeplitz operators [Formula: see text] with [Formula: see text] for some symmetric permutation matrix [Formula: see text]. Surprisingly, these operators [Formula: see text] are the only ones that are complex symmetric monomial Toeplitz operators on the unit bidisk.

Finite sum of weighted composition operators with closed range

In this paper, first we characterize closedness of range of the finite sum of weighted composition operators between different Lp-spaces. Then we discuss polar decomposition and invertibility of these operators.

Generalized weighted composition operators on weighted Hardy spaces

Generalized weighted composition operators on weighted Hardy spaces

Weighted composition operators preserving various Lipschitz constants

Weighted composition operators preserving various Lipschitz constants

Order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weights

Order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weights

Spectral properties of weighted composition operators on Hol(\mathbb{D}) induced by rotations

Spectral properties of weighted composition operators on Hol(\mathbb{D}) induced by rotations

Differences weighted composition operators acting between kind of weighted Bergman-type spaces and the Bers-type space -I-

<abstract><p>Let $ \mathcal{O}(\mathbb{D}) $ denote the class of all analytic or holomorphic functions on the open unit disk $ \mathbb{D} $ of $ \mathbb{C} $. Let $ \varphi $ and $ \psi $ are an analytic self-maps of $ \mathbb{D} $ and $ u, v\in \mathcal{O}(\mathbb{D}). $ The difference of two weighted composition operators is defined by</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ T_{\varphi, \psi}f(z): = \bigg(W_{\varphi, \;u}f- W_{\psi, \;v}f\bigg)(z) = u (z)(f\circ \varphi)(z) -v(z)(f\circ \psi)(z), \ f \in \mathcal{O}(\mathbb{D})\;\hbox{and}\;z\in \mathbb{D}. $\end{document} </tex-math></disp-formula></p> <p>The boundedness and compactness of the differences of two weighted composition operators from $ {\cal H}_{\alpha}^\infty(\mathbb{D}) $ spaces into $ \mathcal{N}_{K}(\mathbb{D}) $ spaces (resp. from $ \mathcal{N}_{K}(\mathbb{D}) $ into $ {\cal H}_{\alpha}^\infty (\mathbb{D}) $) are investigate in this paper.</p></abstract>

Sums of generalized weighted composition operators from the analytic Besov space into the Bloch space

Sums of generalized weighted composition operators from the analytic Besov space into the Bloch space

2-complex symmetric weighted composition operators on Fock space

<abstract><p>The aim of the present paper is to completely characterize 2-complex symmetric weighted composition operators $ W_{e^{\overline{p}z, az+b}} $ with the conjugations $ C $ and $ C_{r, s, t} $ defined by $ Cf(z) = \overline{f(\bar{z})} $ and $ C_{r, s, t}f(z) = te^{sz}\overline{f(\overline{rz+s})} $ on Fock space by building the relations between the parameters $ a $, $ b $, $ p $, $ r $, $ s $ and $ t $. Some examples of such operators are also given.</p></abstract>

Компактность линейных операторов на квазибанаховых пространствах голоморфных функций

We state conditions under which some classical operators acting from abstract quasi-Banach spaces of functions holomorphic in a plain domain into a weighted space of the same functions with sup-norm are compact. It is obtained abstract criteria for the compactness of a linear operator on an arbitrary quasi-Banach space which are stated in terms of delta-functions and formulate their realizations for both classical and generalized Fock spaces. The above results are applied to the weighted composition operator. It is established some conditions for the compactness of this operator which are given in terms of norms of delta-functions in the corresponding dual spaces. These results are essential generalizations of the known Zorboska’s ones. Namely, we significantly extended the class of weighted spaces of holomorphic functions with uniform norms for which one can state some conditions for the compactness of an arbitrary linear operator or the weighted composition operator.

Weighted Composition Operators between Bergman Spaces with Exponential Weights

Weighted Composition Operators between Bergman Spaces with Exponential Weights

Generators of C0-semigroups of weighted composition operators

We prove that in a large class of Banach spaces of analytic functions in the unit disc ⅅ an (unbounded) operator Af = G · f′ + g · f with G, g analytic in ⅅ generates a C0-semigroup of weighted composition operators if and only if it generates a C0-semigroup. Particular instances of such spaces are the classical Hardy spaces. Our result generalizes previous results in this context and it is related to cocycles of flows of analytic functions on Banach spaces. Likewise, for a large class of non-separable Banach spaces X of analytic functions in ⅅ contained in the Bloch space, we prove that no non-trivial holomorphic flow induces a C0-semigroup of weighted composition operators on X. This generalizes previous results in [7] and [1] regarding C0-semigroup of (unweighted) composition operators.

Compactness and weak compactness of weighted composition operators on BMOA

We show that a weighted composition operator W ψ , φ {W_{\psi ,\varphi }} is compact on BMOA precisely when it is unconditionally converging. As a direct consequence to this result we deduce that all weakly compact or completely continuous weighted composition operators on BMOA are compact. The proof of this result is based on a new simplified function-theoretic characterization of the compactness of weighted composition operators on BMOA.

Spectrum of weighted composition operators part VIII lower semi-Fredholm spectrum of weighted composition operators on C(K). The case of non-invertible surjections

Spectrum of weighted composition operators part VIII lower semi-Fredholm spectrum of weighted composition operators on C(K). The case of non-invertible surjections

Weighted composition operators on discrete weighted Banach spaces

We study weighted composition operators on weighted Banach spaces over unbounded, locally finite metric spaces. We characterize the operators that are bounded, compact, being bounded below, having closed range, invertible, being a (surjective) isometry, and are Fredholm. Several examples are presented illustrating the diversity of such operators.

Norms and Essential Norms of Differences of Weighted Composition Operators

Norms and Essential Norms of Differences of Weighted Composition Operators

Weighted Composition Operators between the Bloch Type Space and the Hardy Space on the Unit Ball of Complex Banach Spaces

Let X be a finite or infinite dimensional complex Banach space. We characterize the bounded weighted composition operators between the Bloch type space and the Hardy space on the unit ball of X, extending several known results for finite dimensional domains.

Weighted composition operators from the Besov space into nth weighted type spaces

Abstract Let φ be an analytic self-map of the open unit disk 𝔻 in the complex plane ℂ and u be an analytic function on 𝔻. The weighted composition operator is defined on the space H(𝔻) of analytic functions on 𝔻 by u C φ f = u ⋅ ( f ∘ φ ) , f ∈ H ( D ) . $$u{C_\varphi }f = u \cdot \left( {f \circ \varphi } \right),\quad f \in H\left(D\right).$$ The boundedness and the compactness of weighted composition operators from the Besov space into nth weighted type spaces are given in this work.

Monomial operators

We study monomial operators on \(L^2[0, 1]\), that is bounded linear operators that map each monomial \(x^n\) to a multiple of \(x^{pn}\) for some \(p_n\). We show that they are all unitarily equivalent to weighted composition operators on a Hardy space. We characterize what sequences \(p_n\) can arise. In the case that \(p_n\) is a fixed translation of n, we give a criterion for boundedness of the operator.

Invertible and Isometric Weighted Composition Operators

We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces. For the spaces of analytic functions in the disk whose norm is given in terms of a natural seminorm (such as the typical spaces given in terms of derivatives), we describe all surjective weighted composition operators that are isometric. This generalizes a number of known results.