Complex Symmetric Weighted Composition Operators Research Articles

Real symmetric, unitary, and complex symmetric weighted composition operators on Bergman spaces of polydisk

In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators are not assumed to be bounded. The properties of weighted composition operators such as real symmetry, unitariness, complex symmetry, are characterized fully in simple algebraic terms, involving their symbols. As it turns out, a weighted composition operator having a symmetric structure must be bounded. We also obtain the interesting consequence that real symmetric weighted composition operators are complex symmetric corresponding an adapted and highly relevant conjugation.

Binormal and complex symmetric weighted composition operators on the Fock Space over $\mathbb{C}$

In this paper, we give simple characterization of binormal weighted composition operators $C_{\psi, \phi}$ on the Fock space over $\mathbb{C}$ where weight function is of the form $\psi(\zeta) = e^{\langle \zeta, c \rangle}$ for some $c \in \mathbb{C}$. We derive conditions for $C_{\phi}$ to be binormal such that $C^*_{\phi}C_{\phi}$ and $C^*_{\phi} + C_{\phi}$ commute. Finally we give some simple characterization of binormal weighted composition operator to be complex symmetric.

Complex symmetric weighted composition operators on Bergman spaces and Lebesgue spaces

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of conjugations. As it turns out, weighted composition operators enhanced by a symmetry must be bounded. Hermitian, and unitary weighted composition operators are proven to be complex symmetric with respect to an adapted and highly relevant conjugation. We classify which the linear fractional functions give rise to the complex symmetry of bounded composition operators. We end the paper with a natural link to complex symmetry in Lebesgue space.

Complex symmetric weighted composition operators on weighted Hardy space

Complex symmetric weighted composition operators on weighted Hardy space

Complex symmetric composition operators on the Newton space

A conjecture posed by MacDonald and Rosenthal states the composition operator Cφ acting on the Newton space N2(P) induced by φ(z)=mz+m−12 is bounded, where m∈(0,1). Our first result is proving that the aforementioned conjecture holds. We investigate complex symmetry of composition operators acting on the Newton space, which is different from that on the Hardy space. In addition, normality and co-isometry of composition operators are studied. Finally, we consider complex symmetric weighted composition operators.

English

This paper identifies a class of complex symmetric weighted composition operators on H2(D) that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional.

Complex symmetric weighted composition operators on Dirichlet spaces and Hardy spaces in the unit ball

In this paper, we investigate when weighted composition operators acting on Dirichlet spaces [Formula: see text] are complex symmetric with respect to some special conjugations. We then provide some characterizations of Hermitian weighted composition operators on [Formula: see text]. Furthermore, we give a sufficient and necessary condition for [Formula: see text]-symmetric weighted composition operators on Hardy spaces [Formula: see text] to be unitary or Hermitian, then some new examples of complex symmetric weighted composition operators on [Formula: see text] are obtained. We also discuss the normality of complex symmetric weighted composition operators on [Formula: see text].

Complex symmetric weighted composition operators on the space

In this paper we study the complex symmetric structure of the weighted composition operator on the Hilbert space . We provide some properties of this space and then find some characterizations of symbols φ and ψ so that is complex symmetric with a special conjugation.

Complex symmetric weighted composition operators in several variables

In this paper, we study the complex symmetric weighted composition operators on the Hilbert space Hs of analytic functions over the open unit ball with reproducing kernels Kws(z)=(1−〈z,w〉)−s, where s∈N+. We completely characterize complex symmetric weighted composition operators with respect to two important conjugations JV and Jσ, which include Hermitian weighted composition operators and normal weighted composition operators appeared in [17]. Surprisingly, they are essential representatives of general conjugations of the form Cψ,φJ, where Cψ,φ is unitary and J-symmetric. Indeed, these complex symmetric weighted composition operators can only be divided into two classes. The size estimates and some other properties of these complex symmetric weighted composition operators are obtained. Moreover, involutive weighted composition operators are completely characterized too. As an application, we construct concrete conjugations for the involutive composition operators, which solves a problem raised by Garcia and Hammond in a general case.

Complex symmetric weighted composition operators

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

Complex symmetric weighted composition operators on [formula omitted

We study the complex symmetric structure of weighted composition operators of the form Wψ,φ on the Hilbert space Hγ(D) of holomorphic functions over the open unit disk D with reproducing kernels Kw(γ)=(1−w‾z)−γ, where γ∈N. First, we consider conjugations on Hγ(D) of the form Au,vf=u⋅f∘v‾‾ (such conjugations are also known as weighted composition conjugations) and characterize them into two classes, denoted by C1 and C2. Then, we obtain explicit conditions for Wψ,φ when it is C1-symmetric and C2-symmetric respectively.

Complex symmetric weighted composition operators on the Fock space in several variables

ABSTRACTWe characterize all selfadjoint as well as all unitary anti-linear weighted composition operators acting on the Fock space . Then we obtain a complete description of anti-linear weighted composition operators that are conjugations. These results allow us to determine which bounded linear weighted composition operators can be complex symmetric on .

Complex symmetry of weighted composition operators in several variables

In this paper, we investigate analytic symbols [Formula: see text] and [Formula: see text] when the weighted composition operator [Formula: see text] is complex symmetric on general function space [Formula: see text]. As applications, we characterize completely the compactness, normality and isometry of complex symmetric weighted composition operators. Especially, we show that the equivalence of compactness and Hilbert–Schmidtness, and the existence of non-normal complex symmetric operators for such operators, which answers one open problem raised by Noor in [On an example of a complex symmetric composition operators on [Formula: see text], J. Funct. Anal. 269 (2015) 1899–1901] for higher dimensional case.

Complex symmetric weighted composition operators on [formula omitted

In this paper we study complex symmetric weighted composition operators on the Hardy space. We provide some characterizations of ψ and φ when a weighted composition operator Wψ,φ is complex symmetric. We investigate which combinations of weights ψ and maps of the open unit disk φ give rise to complex symmetric weighted composition operators with a special conjugation. As some applications, we obtain several examples for nonnormal complex symmetric operators. In addition, we give spectral properties of complex symmetric weighted composition operators. We examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is Hilbert–Schmidt. Finally, we consider cyclicity, hypercyclicity, and the single-valued extension property for complex symmetric weighted composition operators.