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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 J f (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. [ABSTRACT FROM AUTHOR]

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.

We obtain the norm and essential norm estimates for the difference of two weighted composition operators from a weighted Bergman space A α p into a Lebesgue space L q (μ) , where 0 < p ≤ q , α > - 1 and μ is a positive Borel measure on the unit disk of C . The weights of the weighted maps in this paper are not necessarily analytic or bounded. Consequently, characterizations for the boundedness and compactness of the difference operator are established. [ABSTRACT FROM AUTHOR]

The spectrum of a weighted composition operator C ψ , φ that is induced by an automorphism has been investigated for over 50 years. However, many results are got only under the condition that the weight function ψ is continuous up to the boundary. In this paper we study the spectra and essential spectra of C ψ , φ on weighted Bergman spaces when φ is an elliptic automorphism, without the assumption that ψ is continuous up to the boundary. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the compact differences of weighted composition operators on the standard weighted Bergman spaces. Some necessary and sufficient conditions for the differences of weighted composition operators to be compact are given, which extends Moorhouse’s results in (J. Funct. Anal. 219:70-92, 2005).

In this paper we will show how the boundedness condition for the weighted composition operators on a class of spaces of analytic functions on the open right complex half-plane called Zen spaces (which include the Hardy spaces and weighted Bergman spaces) can be stated in terms of Carleson measures and Bergman kernels. In Hilbertian setting we will also show how the norms of causal weighted composition operators on these spaces are related to each other and use it to show that an (unweighted) composition operatorCφ is bounded on a Zen space if and only if φ has a finite angular derivative at infinity. Finally, we will show that there is no compact composition operator on Zen spaces. [ABSTRACT FROM AUTHOR]

Let be an analytic map and ϕ an analytic self-map of the open unit disk D. Such maps induce the so-calledweighted composition operator Cϕ,Ψ : H(D) → H(D), f →Ψ (f º ϕ), where H(D) denotes the set of all analytic functions on D. We study when such an operator acting between different weighted Bergman spaces has a closed range. [ABSTRACT FROM AUTHOR]

In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space. [ABSTRACT FROM AUTHOR]

Recently, Gao et al. (Chin Ann Math 37B:585-594, 2016) proved a sufficient condition for order boundedness of a weighted composition operator acting between Dirichlet spaces. In this paper, we prove that their condition is a necessary and sufficient condition for order boundedness of a weighted composition operator acting between these spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider the compact differences of weighted composition operators on the standard weighted Bergman spaces. Some necessary and sufficient conditions for the differences of weighted composition operators to be compact are given, which extends Moorhouse's results in (J. Funct. Anal. 219:70-92, 2005). [ABSTRACT FROM AUTHOR]

Let $$\varphi $$ be an arbitrary linear-fractional self-map of the unit disk $${\mathbb {D}}$$ and consider the composition operator $$C_{-1, \varphi }$$ and the Toeplitz operator $$T_{-1,z}$$ on the Hardy space $$H^2$$ and the corresponding operators $$C_{\alpha , \varphi }$$ and $$T_{\alpha , z}$$ on the weighted Bergman spaces $$A^2_{\alpha }$$ for $$\alpha >-1$$ . We prove that the unital C $$^*$$ -algebra $$C^*(T_{\alpha , z}, C_{\alpha , \varphi })$$ generated by $$T_{\alpha , z}$$ and $$C_{\alpha , \varphi }$$ is unitarily equivalent to $$C^*(T_{-1, z}, C_{-1, \varphi }),$$ which extends a known result for automorphism-induced composition operators. For maps $$\varphi $$ that are not automorphisms of $${\mathbb {D}}$$ , we show that $$C^*(C_{\alpha , \varphi }, {\mathcal {K}}_{\alpha })$$ is unitarily equivalent to $$C^*(C_{-1, \varphi }, {\mathcal {K}}_{-1})$$ , where $${\mathcal {K}}_{\alpha }$$ and $${\mathcal {K}}_{-1}$$ denote the ideals of compact operators on $$A^2_{\alpha }$$ and $$H^2$$ , respectively, and apply existing structure theorems for $$C^*(C_{-1, \varphi }, {\mathcal {K}}_{-1})/{\mathcal {K}}_{-1}$$ to describe the structure of $$C^*(C_{\alpha , \varphi }, {\mathcal {K}}_{\alpha })/\mathcal {K_{\alpha }}$$ , up to isomorphism. We also establish a unitary equivalence between related weighted composition operators induced by maps $$\varphi $$ that fix a point on the unit circle. [ABSTRACT FROM AUTHOR]

In this work, we provide an approximation of the essential norm of the weighted composition operators acting on a Hilbert function space and mapping into a Zygmund-type space, and give characterizations of the boundedness and compactness of such operators. Our results apply to a large class of weighted Hardy spaces, including the Hardy space H, the weighted Bergman space $${A^2_\alpha \,\, (\alpha \geq 1)}$$ , and the logarithmic Bergman space $${A^2_{\rm log}}$$ . [ABSTRACT FROM AUTHOR]

In this paper, we estimate the essential norm of a weighted composition operator from Hardy space to weighted Bergman space on the unit ball in the complex N-dimensional Euclidean space. In our results, we use Carleson type measures and certain integral operators to estimate the essential norm. [ABSTRACT FROM AUTHOR]

This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product. [ABSTRACT FROM AUTHOR]

This paper shows that the boundedness of a weighted composition operator on the Hardy-Hilbert space on the disc or half-plane implies its boundedness on a class of related spaces, including weighted Bergman spaces. The methods used involve the study of lower-triangular and causal operators. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the boundedness and compactness of the weighted composition operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators. [ABSTRACT FROM AUTHOR]

Weighted composition operators have been related to products of composition operators and their adjoints and to isometries of Hardy spaces. In this paper, Hermitian weighted composition operators on weighted Hardy spaces of the unit disk are studied. In particular, necessary conditions are provided for a weighted composition operator to be Hermitian on such spaces. On weighted Hardy spaces for which the kernel functions are $${(1 - \overline{w}z)^{-\kappa}}$$ for κ ≥ 1, including the standard weight Bergman spaces, the Hermitian weighted composition operators are explicitly identified and their spectra and spectral decompositions are described. Some of these Hermitian operators are part of a family of closely related normal weighted composition operators. In addition, as a consequence of the properties of weighted composition operators, we compute the extremal functions for the subspaces associated with the usual atomic inner functions for these weighted Bergman spaces and we also get explicit formulas for the projections of the kernel functions on these subspaces. [ABSTRACT FROM AUTHOR]

In this paper, we limit our analysis to the difference of the weighted composition operators acting from the Hardy space to weighted-type space in the unit ball of ℂ, and give some necessary and sufficient conditions for their boundedness or compactness. The results generalize the corresponding results on the single weighted composition operators and on the differences of composition operators, for example, M. Lindström and E. Wolf: Essential norm of the difference of weighted composition operators. Monatsh. Math. 153 (2008), 133-143. [ABSTRACT FROM AUTHOR]

Let φ and φ be holomorphic self-maps of the unit polydisk $\mathbb{D}^N$ , and let u and u be holomorphic functions on $\mathbb{D}^N$ . We characterize the boundedness and compactness of the difference of weighted composition operators W and W from the weighted Bergman space $A_{\vec \alpha }^p$ , 0 < p < ∞, $\vec \alpha = \left( {\alpha _1 , \ldots ,\alpha _{\rm N} } \right)$ , α > −1, j = 1,..., N, to the weighted-type space H of holomorphic functions on the unit polydisk $\mathbb{D}^N$ in terms of inducing symbols φ, φ, u, and u. [ABSTRACT FROM AUTHOR]

Abstract: We characterize the compactness of differences of weighted composition operators from the weighted Bergman space , 0< p <∞, α >−1, to the weighted-type space of analytic functions on the open unit disk in terms of inducing symbols and . For the case 1< p <∞ we find an asymptotically equivalent expression to the essential norm of these operators. [Copyright &y& Elsevier]

Abstract: Let be a bounded symmetric domain, the class of all holomorphic functions on and . Operator norm of the multiplication operator on the weighted Bergman space , as well as of weighted composition operator from to a weighted-type space are calculated. [Copyright &y& Elsevier]

Abstract: Let be the class of all holomorphic functions on the set and . We calculate operator norms of the multiplication operators , on the weighted Bergman space , as well as on the Hardy space , where X is the unit polydisk or the unit ball in . We also calculate the norm of the weighted composition operator from the weighted Bergman space , and the Hardy space , to a weighted-type space on the unit polydisk. [Copyright &y& Elsevier]

Abstract: In this paper, we study the weighted composition operators between weighted Bergman spaces and Hardy spaces on the unit ball of . We characterize the boundedness and the compactness of the weighted composition operators and . [Copyright &y& Elsevier]

The spectra and essential spectra of some weighted composition operators arising from non-automorphic parabolic self-maps of the unit disc acting on a class of Banach spaces- not necessarily reflexive- of analytic functions is shown to be a spiral-like set, as it happens in the cases treated earlier. [ABSTRACT FROM AUTHOR]