scholarly journals Isometric multiplication operators and weighted composition operators of BMOA

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ligang Geng
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

AbstractLet u be an analytic function in the unit disk $\mathbb{D}$ D and φ be an analytic self-map of $\mathbb{D}$ D . We give characterizations of the symbols u and φ for which the multiplication operator $M_{u}$ M u and the weighted composition operator $M_{u,\varphi }$ M u , φ are isometries of BMOA.

scholarly journals Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Sei-Ichiro Ueki ◽  
Luo Luo
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Multiplication Operator ◽  
Essential Norm ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

We estimate the essential norm of a compact weighted composition operator acting between different Hardy spaces of the unit ball in . Also we will discuss a compact multiplication operator between Hardy spaces.

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 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.

scholarly journals Spectrums and Uniform Mean Ergodicity of Weighted Composition Operators on Fock Spaces

2021 ◽  
Author(s):  
Werkaferahu Seyoum ◽  
Tesfa Mengestie
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Linear Expansion ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Fock Spaces ◽  
Ergodic Properties ◽  
Weighted Composition ◽  
Mean Ergodicity ◽  
Power Bounded

AbstractFor holomorphic pairs of symbols $$(u, \psi )$$ ( u , ψ ) , we study various structures of the weighted composition operator $$ W_{(u,\psi )} f= u \cdot f(\psi )$$ W ( u , ψ ) f = u · f ( ψ ) defined on the Fock spaces $$\mathcal {F}_p$$ F p . We have identified operators $$W_{(u,\psi )}$$ W ( u , ψ ) that have power-bounded and uniformly mean ergodic properties on the spaces. These properties are described in terms of easy to apply conditions relying on the values |u(0)| and $$|u(\frac{b}{1-a})|$$ | u ( b 1 - a ) | , where a and b are coefficients from linear expansion of the symbol $$\psi $$ ψ . The spectrum of the operators is also determined and applied further to prove results about uniform mean ergodicity.

scholarly journals ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE

2009 ◽  
Vol 79 (1) ◽  
pp. 147-160 ◽  
Author(s):  
ROBERT F. ALLEN ◽  
FLAVIA COLONNA
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bloch Space ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

AbstractIn this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.

scholarly journals Supercyclicity and Resolvent Condition for Weighted Composition Operators

2021 ◽  
Author(s):  
Tesfa Mengestie ◽  
Werkaferahu Seyoum
Keyword(s):  
Growth Condition ◽  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Holomorphic Maps ◽  
Fock Spaces ◽  
Resolvent Condition ◽  
Weighted Composition ◽  
Resolvent Growth

AbstractFor pairs of holomorphic maps $$(u,\psi )$$ ( u , ψ ) on the complex plane, we study some dynamical properties of the weighted composition operator $$W_{(u,\psi )}$$ W ( u , ψ ) on the Fock spaces. We prove that no weighted composition operator on the Fock spaces is supercyclic. Conditions under which the operators satisfy the Ritt’s resolvent growth condition are also identified. In particular, we show that a non-trivial composition operator on the Fock spaces satisfies such a growth condition if and only if it is compact.

scholarly journals WEIGHTED COMPOSITION OPERATORS FROM F(p, q, s) TO BLOCH TYPE SPACES ON THE UNIT BALL

2008 ◽  
Vol 19 (08) ◽  
pp. 899-926 ◽  
Author(s):  
ZE-HUA ZHOU ◽  
REN-YU CHEN
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Type Spaces ◽  
Weighted Composition

Let ϕ(z) = (ϕ1(z),…,ϕn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of ℂn. Let 0 < p, s < +∞, -n - 1 < q < +∞, q+s > -1 and α ≥ 0, this paper characterizes boundedness and compactness of weighted composition operator Wψ,ϕ induced by ϕ and ψ between the space F(p, q, s) and α-Bloch space [Formula: see text].

scholarly journals On the Norm of Certain Weighted Composition Operators on the Hardy Space

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
M. Haji Shaabani ◽  
B. Khani Robati
Keyword(s):  
Hardy Space ◽  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Special Case

We obtain a representation for the norm of certain compact weighted composition operator on the Hardy space , whenever and . We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on and . Moreover, we characterize the norm and essential norm of such operators in a special case.

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 on Some Weighted Spaces in the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaohong Fu ◽  
Xiangling Zhu
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Weighted Composition Operators ◽  
Weighted Composition

LetBnbe the unit ball ofCn,H(Bn)the space of all holomorphic functions inBn. Letu∈H(Bn)andαbe a holomorphic self-map ofBn. Forf∈H(Bn), the weigthed composition operatoruCαis defined by(uCαf)(z)=u(z)f(α(z)),z∈Bn.The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.

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