scholarly journals Normal and quasinormal weighted composition operators

1991 ◽  
Vol 33 (3) ◽  
pp. 275-279 ◽  
Author(s):  
James T. Campbell ◽  
Mary Embry-Wardrop ◽  
Richard J. Fleming ◽  
S. K. Narayan
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Necessary And Sufficient

In their paper [1], Campbell and Jamison attempted to give necessary and sufficient conditions for a weighted composition operator on an L2 space to be normal, and to be quasinormal. Those conditions, specifically Theorems I and II of that paper, are not valid (see [2] for precise comments on the other results in that paper). In this paper we present a counterexample to those theorems and state and prove characterizations of quasinormality (Theorem 1 below) and normality (Theorem 2 and Corollary 3 below). We also discuss additional examples and information concerning normal weighted composition operators which contribute to the further understanding of this class.

scholarly journals Weighted composition operators from Bloch-type into Bers-type spaces

2021 ◽  
Vol 29 (2) ◽  
pp. 243-250
Author(s):  
HAMID VAEZI ◽  
MOHAMAD NAGHLISAR
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Type Space ◽  
Bloch Type Space ◽  
Type Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient

In this paper we consider the weighted composition operator uC_{\varphi} from Bloch-type space B^{\alpha} into Bers-type space H_{\beta}^{\infty}, in three cases, \alpha>1, \alpha=1 and \alpha<1. We give the necessary and sufficient conditions for boundedness and compactness of the above operator.

Weighted composition operators between Fock spaces ℱ∞(ℂ) and ℱp(ℂ)

2019 ◽  
Vol 30 (03) ◽  
pp. 1950015 ◽  
Author(s):  
Le Hai Khoi ◽  
Le Thi Hong Thom ◽  
Pham Trong Tien
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Connected Components ◽  
Weighted Composition Operators ◽  
Fock Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient ◽  
Path Connected

In this paper, we establish necessary and sufficient conditions for boundedness and compactness of weighted composition operators acting between Fock spaces [Formula: see text] and [Formula: see text]. We also give complete descriptions of path connected components for the space of composition operators and the space of nonzero weighted composition operators in this context.

scholarly journals New additive results for Cauchy dual and MP-inverse of weighted composition operators

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2215-2230
Author(s):  
Morteza Sohrabi
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Necessary And Sufficient

In this paper, we prove some basic results for Cauchy dual of weighted composition operators. Also we introduce some new classes of operators, called ?-hyponormal, ?-quasi-hyponormal, and we provide necessary and sufficient conditions for Cauchy dual and MP-inverse of weighted composition operators on L2(?) to belong to these classes. In addition, we study the complex symmetry of these types of operators. Moreover, some examples are provided to illustrate the obtained results.

scholarly journals Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces

2020 ◽  
Vol 40 (4) ◽  
pp. 495-507
Author(s):  
Ching-on Lo ◽  
Anthony Wai-keung Loh
Keyword(s):  
Hardy Space ◽  
Unit Disk ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Weighted Composition

Let \(u\) and \(\varphi\) be two analytic functions on the unit disk \(\mathbb{D}\) such that \(\varphi(\mathbb{D}) \subset \mathbb{D}\). A weighted composition operator \(uC_{\varphi}\) induced by \(u\) and \(\varphi\) is defined on \(H^2\), the Hardy space of \(\mathbb{D}\), by \(uC_{\varphi}f := u \cdot f \circ \varphi\) for every \(f\) in \(H^2\). We obtain sufficient conditions for Hilbert-Schmidtness of \(uC_{\varphi}\) on \(H^2\) in terms of function-theoretic properties of \(u\) and \(\varphi\). Moreover, we characterize Hilbert-Schmidt difference of two weighted composition operators on \(H^2\).

scholarly journals Basic properties of finite sum of weighted composition operators

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 4005-4019
Author(s):  
Abolghasem Alishahi ◽  
Saeedeh Shamsigamchi ◽  
Ali Ebadian
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Lp Spaces ◽  
Basic Properties ◽  
Weighted Composition ◽  
Finite Sums ◽  
Finite Sum ◽  
Necessary And Sufficient

In this paper,we continue the study of finite sum of weighted composition operators between different Lp-spaces that was investigated by Jabbarzadeh and Estaremi in 2012. Indeed, we first obtain some necessary and sufficient conditions for boundedness of the finite sums of weighted composition operators between distinct Lp-spaces. In the sequel, we investigate the compactness of finite sum of weighted composition operators. By using theorems of boundedness and compactness, we estimate the essential norms of these operators. Finally, some examples to illustrate the main results are given.

scholarly journals Weighted Composition Operators fromH∞to the Bloch Space on the Polydisc

2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Songxiao Li ◽  
Stevo Stevic
Keyword(s):  
Holomorphic Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Necessary And Sufficient ◽  
Bounded Holomorphic

LetDnbe the unit polydisc ofℂn,ϕ(z)=(ϕ1(z),…,ϕn(z))be a holomorphic self-map ofDn, andψ(z)a holomorphic function onDn. LetH(Dn)denote the space of all holomorphic functions with domainDn,H∞(Dn)the space of all bounded holomorphic functions onDn, andB(Dn)the Bloch space, that is,B(Dn)={f∈H(Dn)|‖f‖B=|f(0)|+supz∈Dn∑k=1n|(∂f/∂zk)(z)|(1−|zk|2)<+∞}. We give necessary and sufficient conditions for the weighted composition operatorψCϕinduced byϕ(z)andψ(z)to be bounded and compact fromH∞(Dn)to the Bloch spaceB(Dn).

scholarly journals Non-Weakly Supercyclic Weighted Composition Operators

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Z. Kamali ◽  
K. Hedayatian ◽  
B. Khani Robati
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disc ◽  
Space Of Analytic Functions ◽  
Weighted Composition ◽  
Necessary And Sufficient

We give sufficient conditions under which a weighted composition operator on a Hilbert space of analytic functions is not weakly supercyclic. Also, we give some necessary and sufficient conditions for hypercyclicity and supercyclicity of weighted composition operators on the space of analytic functions on the open unit disc.

WEIGHTED COMPOSITION OPERATORS BETWEEN H∞ AND GENERALLY WEIGHTED BLOCH SPACES ON POLYDISKS

2010 ◽  
Vol 21 (05) ◽  
pp. 687-699 ◽  
Author(s):  
HAIYING LI ◽  
PEIDE LIU
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Unit Polydisk ◽  
Necessary And Sufficient ◽  
Bounded Holomorphic

Let Un be the unit polydisk of Cn, φ(z) = (φ1(z),φ2(z),…,φn(z)) be a holomorphic self-map of Un and ψ be a holomorphic function on Un. H∞(Un) is the space of all bounded holomorphic functions on Un and by a generally weighted Bloch space we mean [Formula: see text]. We give necessary and sufficient conditions of the boundedness and compactness of the weighted composition operator ψCφ between H∞(Un) and [Formula: see text].

scholarly journals Antinormal Weighted Composition Operators

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Dilip Kumar ◽  
Harish Chandra
Keyword(s):  
Hilbert Space ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Counting Measure ◽  
Power Set ◽  
Weighted Composition ◽  
Necessary And Sufficient ◽  
Positive Integers

Letl2=L2N,μ, whereNis set of all positive integers andμis the counting measure whoseσ-algebra is the power set ofN. In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert spacel2. We also determine a class of antinormal weighted composition operators on Hardy spaceH2D.

Weighted Composition Operators on Bergman and Dirichlet Spaces

1997 ◽  
Vol 4 (4) ◽  
pp. 373-383
Author(s):  
G. Mirzakarimi ◽  
K. Seddighi
Keyword(s):  
Composition Operator ◽  
Hilbert Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Dirichlet Spaces ◽  
Weighted Dirichlet Spaces ◽  
Weighted Composition ◽  
Functional Hilbert Spaces

Abstract Let 𝐻(Ω) denote a functional Hilbert space of analytic functions on a domain Ω. Let 𝑤 : Ω → 𝐂 and ϕ : Ω → Ω be such that 𝑤 𝑓 ○ ϕ is in 𝐻(Ω) for every 𝑓 in 𝐻(Ω). The operator 𝑤𝐶 ϕ Given by 𝑓 → 𝑤 𝑓 ○ ϕ is called a weighted composition operator on 𝐻(Ω). In this paper we characterize such operators and those for which (𝑤𝐶 ϕ )* is a composition operator. Compact weighted composition operators on some functional Hilbert spaces are also characterized. We give sufficient conditions for the compactness of such operators on weighted Dirichlet spaces.

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