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.     

Quasisymmetry of weakly quasisymmetric homeomorphisms

This paper is devoted to the study of weakly quasisymmetric homeomorphisms. We investigate under what conditions a weakly H-quasisymmetric map is actually quasisymmetric. As a consequence, we deduce conditions under which the inverse and composition of weakly quasisymmetric homeomorphisms are also weakly quasisymmetric.     

Riemann–Hilbert-type problems for Bitsadze equations with strong singularities in low-order coefficients

For the Bitsadze equation with low-order coefficients admitting a power singularity at a fixed point of the domain, we investigate a boundary-value problem with the Riemann–Hilbert data for the solution itself and for its partial derivatives. We prove the Fredholm solvability of that problem and present its index formula.     

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.     

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.

     

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.

     

Invertible weighted composition operators

A weighted composition operator Cψ,φ takes an analytic map f on the open unit disc of the complex plane to the analytic map ψ⋅f°φ where φ is an analytic map of the open unit disc into itself and ψ is an analytic map on the open unit disc. This paper studies the invertibility of such operators. The two maps ψ and φ are characterized when Cψ,φ acts on the Hardy-Hilbert space of the unit disc H²(D). Depending upon the nature of the fixed points of φ spectra are then investigated.     

Fredholm weighted composition operators

We characterize the Fredholm weighted composition operators onC(X). In particular, ifX is a set with some regular property like intervals or balls inR ⁿ , our characterization implies that a weighted composition operator is Fredholm if and only if it is invertible. This equivalence is true for weighted composition operators onL ^p (), where is a nonatomic measure (1p<).     

Complex symmetric operators and applications

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.

     

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.     

Approximation numbers of weighted composition operators

We study the approximation numbers of weighted composition operators $f?w?(f°\phi )$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight w can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples).