Weighted Composition Operators Research Articles

Order-Bounded Difference in Weighted Composition Operators Between Fock Spaces

There are two aims in this paper. The first aim is to characterize the order-bounded weighted composition operators between Fock spaces, and the second is to further characterize the order-bounded difference in weighted composition operators between Fock spaces. At the same time, six examples are given to illustrate the relations between boundedness and ordered boundedness. Moreover, an interesting result is found that differences in weighted composition operators defined by some special weighted functions and symbol functions are order-bounded between Fock spaces if and only if each weighted composition operator is compact between Fock spaces. Finally, two open questions are also put forward for converting larger Fock spaces into smaller ones.

Remark on square roots of self-adjoint weighted composition operators on H2

In this paper, we study square roots of self-adjoint weighted composition operators on H2. More precisely, we focus on square roots Wf,φ of a self-adjoint operator Wg,ψ=Wf,φ2 when φ is a linear fractional selfmap of D. We also investigate several properties of such Wf,φ. Finally, we show that the square roots Wf,φ may be other, nonself-adjoint weighted composition operators and have nontrivial invariant subspaces.

Finite Sum of Integral Operators from the Fractional Cauchy Spaces to Bloch-Type and Zygmund-Type Spaces

The family of fractional Cauchy transforms, defined on the open unit disc in the complex plane, is of classical and modern interest. Membership of an analytic function in the family is determined by the requirement that the function can be expressed as an integral of a certain kernel against a complex Borel measure on the disc. Such an integral representation imposes a growth condition on the function and its derivatives. This exposes a connection between the families of Cauchy transforms and familiar spaces of analytic functions, such as the Bloch spaces and the Zygmund space. The notion of a composition operator has been a fruitful area of study. More generally, many authors have studied weighted composition operators, the differentiation operator, integral-type operators, and various products of such operators, acting from one normed linear space of analytic functions to another such space. A common theme of such works is to characterize the operator-theoretic notions of boundedness and compactness in terms of the inducing symbols of the operator. We extend these studies to a specific linear transformation which will be defined as the sum of finitely many integral operators. Our conclusions include a complete characterization of boundedness and compactness of the integral sum, acting from the fractional Cauchy spaces to the Bloch-type and Zygmund-type spaces.

The Spectra of Multiplication Operators and Weighted Composition Operators on Iterated Weighted-Type Banach Spaces of Analytic Functions

This research aims to analyze the spectral of multiplication operators acting on weighted Banach spaces of analytic functions defined on the unit disk. These spaces, denoted by Sn : n ∈ N, include well-known cases such as the Bloch space and the Zygmund space for n = 1 and n = 2, respectively. Additionally, we offer a description of the spectra of weighted composition operators within these spaces. The outline of this paper provides a structured framework for organizing the research, starting from the introduction to the conclusion and references. The main section is to investigate the spectrum of multiplication operators on Sn spaces, and it followed by a section that is designed to build upon the previous one, leading to characterize the spectrum of weighted composition operators on the same spaces.

On the Product of Weighted Composition Operators and Radial Derivative Operators from the Bloch-Type Space into the Bers-Type Space on the Fourth Loo-Keng Hua Domain

Let HEIV be the fourth Loo-Keng Hua domain. We study the boundedness of the product of the weighted composition operator and the radial derivative operator from the Bloch-type space Bα(HEIV) into the Bers-type space Aβ(HEIV) and provide the necessary and sufficient conditions for their boundedness.

Growth Spaces on Circular Domains Taking Values in a Banach Lattice, Embeddings and Composition Operators

We introduce the space of holomorphic growth spaces with values in a Banach lattice. We provide norm and essential norm estimates of the embedding operator, and we completely characterize the bounded and compact embeddings of the growth spaces using vector-valued Carleson measures. As an application, we prove a characterization of weighted composition operators.

Sums of Generalized Weighted Composition Operators from Weighted Bergman Spaces Induced by Doubling Weights into Bloch-Type Spaces

The single generalized weighted composition operator Du,ψn on various spaces of analytic functions has been investigated for decades, i.e., Du,ψnf=u·(f(n)∘ψ), where f∈H(D). However, the study of the finite sum of generalized weighted composition operators with different orders, i.e., PU,ψkf=u0·f∘ψ+u1·f′∘ψ+⋯+uk·f(k)∘ψ, is far from complete. The boundedness, compactness and essential norm of sums of generalized weighted composition operators from weighted Bergman spaces with doubling weights into Bloch-type spaces are investigated. We show a rigidity property of PU,ψk. Specifically, the boundedness and compactness of the sum PU,ψk is equivalent to those of each Dun,ψn, 0≤n≤k.

Weighted Composition Operators between Bers-Type Spaces on Generalized Hua–Cartan–Hartogs Domains

Weighted Composition Operators between Bers-Type Spaces on Generalized Hua–Cartan–Hartogs Domains

Spectrum of weighted composition operators part X: the spectrum and essential spectra of weighted automorphisms of the polydisc algebra

Spectrum of weighted composition operators part X: the spectrum and essential spectra of weighted automorphisms of the polydisc algebra

Linear isometries of [formula omitted]

A complete characterisation is given of all the linear isometries of the Fréchet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of a particular form. Operators similar to an isometry are also classified. Further, the larger class of operators isometric when restricted to one of the defining seminorms is identified. Finally, the spectra of such operators are studied.

Weighted composition operator on Gamma spaces with variable exponent

Weighted composition operator on Gamma spaces with variable exponent

Weighted composition operators on the logarithmic Bloch-Orlicz space.

The boundedness and compactness of weighted composition operators on the logarithmic Bloch-Orlicz space [Formula: see text] are investigated in this paper.

Weighted composition operators that preserve p-frames

We establish the equivalence between being invertible and preserving p-frames for weighted composition operators on the unit disk. Moreover, we obtain the symbol properties of the bounded invertible operators. Based on those results, we prove that for the weighted Bergman spaces Aap(dAα), Besov spaces Bp and weighted Dirichlet spaces Dα2, weighted composition operators preserve p-frames on X if and only if they preserve q-Riesz bases on X⁎, and obtain related application on dynamical sampling of weighted composition operators. Furthermore, we characterize the equivalence between Fredholmness and the invertibility of weighted composition operators.

Complex symmetry in the Fock space of several variables

In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex symmetric with respect to a concrete conjugation. Using this characterization, we study complex symmetric semigroups and their generators. We realize such generators as first-order differential operators.

Closed Range and Preserving Frames of Weighted Composition Operator on Quaternionic Fock Space

Closed Range and Preserving Frames of Weighted Composition Operator on Quaternionic Fock Space

3-Complex Symmetric and Complex Normal Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane

One of the aims of this paper is to characterize 3-complex symmetric weighted composition operators induced by three types of symbols on the weighted Bergman space of the right half-plane with the conjugation Jf(z)=f(z¯)¯. It is well known that the complex symmetry is equivalent to 2-complex symmetry for the weighted composition operators studied in the paper. However, the interesting fact that 3-complex symmetry is not equivalent to 2-complex symmetry for such operators is found in the paper. Finally, the complex normal of such operators on the weighted Bergman space of the right half-plane with the conjugation J is characterized.

Reciprocals of Weighted Composition Operators in $$L^2$$-Spaces

Reciprocals of Weighted Composition Operators in $$L^2$$-Spaces

Ergodic properties of multiplication and weighted composition operators on spaces of holomorphic functions

AbstractWe obtain different results about the mean ergodicity of weighted composition operators when acting on the spaces , , and , where is the open unit ball of a Banach space, as well as about the compactness and the mean ergodicity of the multiplication operator. This study relates these properties of the operators with properties of the symbol and the weight defining such operators.

Essential norm of linear operators from general weighted‐type spaces to Banach spaces and some applications

We present a result concerning the essential norm of linear operators mapping some general weighted‐type spaces of holomorphic functions on the open unit ball in to Banach spaces. As some applications, we compare essential norms of a product‐type operator of integral type and a weighted composition operator between some of the general weighted‐type spaces.

Difference of Weighted Composition Operators Over the Ball

Difference of Weighted Composition Operators Over the Ball