Complex symmetric weighted composition operators

In this paper, we find complex symmetric weighted composition operators with special conjugations. Then we give spectral properties of these complex symmetric weighted composition operators.     

A class of weighted composition operators on the Fock space

ABSTRACT

By applying reproducing kernel techniques, a class of weighted composition operators on the Fock space, which are unitarily equivalent to nonzero constant multiple of composition operators, are characterized completely.     

Compact weighted composition operators on the Hardy space

A weighted composition operator takes an analytic map on the open unit disk of the complex plane to the analytic map , where is an analytic map of the open unit disk into itself and is an analytic map on the open unit disk. This paper studies how the compactness of depends on the interaction between the two maps and .

     

Isometric composition operators on weighted Dirichlet space

We investigate isometric composition operators on the weighted Dirichlet space \({D_\alpha }\) with standard weights \({(1 - {\left| z \right|^2})^\alpha },\alpha > - 1\). The main technique used comes from Martín and Vukoti? who completely characterized the isometric composition operators on the classical Dirichlet space D. We solve some of these but not in general. We also investigate the situation when \({D_\alpha }\) is equipped with another equivalent norm.     

The composition operators on weighted Bloch space

We will characterize the boundedness and compactness of the composition operators on weighted Bloch space B _log = { f ? H(D): sup_{z ? D} (1-| z|²) ( log\frac21-| z|² )| f￠(z)| B_{ \log }= \{ f \in H(D): \sup_{z \in D } (1-\left| z\right|^2) \left( \log \frac{2}{1-\left| z\right|^2} \right)\left| f'(z)\right| < +￥} +\infty \} , where H(D) be the class of all analytic functions on D.     

A note on weighted composition operators on the weighted Bergman space

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.     

Weighted composition operators from the weighted Bergman space to the weighted Hardy space on the unit ball

We investigate the weighted composition operator from the weighted Bergman space into the weighted Hardy space on the unit ball. As a consequence of the investigation, we also give a characterization for the boundedness and compactness of the operator whose the target space is the Hardy space.     

Weighted composition operators on weighted Bergman spaces of bounded symmetric domains

In this paper, we study the weighted compositon operators on weighted Bergman spaces of bounded symmetric domains. The necessary and sufficient conditions for a weighted composition operator W _φψ to be bounded and compact are studied by using the Carleson measure techniques. In the last section, we study the Schatten p-class weighted composition operators.     

Essential norms of weighted composition operators from weighted Bergman space to mixed-norm space on the unit ball

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.     

Schatten class composition operators on weighted Bergman spaces of bounded symmetric domains

Summary We obtain trace ideal criteria for 0A ² () of a Bounded symmetric diomain in _n.     

Hypercyclic property of weighted composition operators

In the present paper we investigate conditions under which a holomorphic self-map of the open unit disk induces a hypercyclic weighted composition operator in the space of holomorphic functions.

     

Invertible weighted composition operators on weighted function spaces

В статье дается харак теризация обратимых весовых операторов композиц ии, определенных на весо вых локально выпуклы х пространствах непре рывных функций и на весовых п ространствах сечени й, задаваемых семейств ом полунорм, являющихся весовыми аналогами равномерн ой нормы.     

Complex symmetric operators and applications II

A bounded linear operator on a complex Hilbert space is called complex symmetric if , where is a conjugation (an isometric, antilinear involution of ). We prove that , where is an auxiliary conjugation commuting with . We consider numerous examples, including the Poincaré-Neumann singular integral (bounded) operator and the Jordan model operator (compressed shift). The decomposition also extends to the class of unbounded -selfadjoint operators, originally introduced by Glazman. In this context, it provides a method for estimating the norms of the resolvents of certain unbounded operators.