scholarly journals Weighted composition operators on functional Hilbert spaces

1985 ◽  
Vol 31 (1) ◽  
pp. 117-126 ◽  
Author(s):  
R.K. Singh ◽  
R. David Chandra Kumar
Keyword(s):  
Hilbert Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Linear Operators ◽  
Weighted Composition Operators ◽  
Bounded Linear ◽  
Atomic Measure ◽  
Weighted Composition ◽  
Functional Hilbert Spaces

Let X be a non-empty set and let H(X) denote a Hibert space of complex-valued functions on X. Let T be a mapping from X to X and θ a mapping from X to C such that for all f in H(X), f ° T is in H(x) and the mappings CT taking f to f ° T and M taking f to θ.f are bounded linear operators on H(X). Then the operator CTMθ is called a weighted composition operator on H(X). This note is a report on the characterization of weighted composition operators on functional Hilbert spaces and the computation of the adjoint of such operators on L2 of an atomic measure space. Also the Fredholm criteria are discussed for such classes of operators.

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.

scholarly journals Invertible Weighted Composition Operators on the Fock Space ofCN

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Liankuo Zhao
Keyword(s):  
Fock Space ◽  
Composition Operators ◽  
Complete Characterization ◽  
Weighted Composition Operators ◽  
Weighted Composition

We give a complete characterization of bounded invertible weighted composition operators on the Fock space ofCN.

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 Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Banach Space ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Weighted Composition

The logarithmic Bloch spaceBlog⁡is the Banach space of analytic functions on the open unit disk&#x1D53B;whose elementsfsatisfy the condition∥f∥=sup⁡z∈&#x1D53B;(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy spaceHp(with1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mappingHpinto the little logarithmic Bloch space defined as the subspace ofBlog⁡consisting of the functionsfsuch thatlim⁡|z|→1(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|=0.

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 WEIGHTED COMPOSITION OPERATORS AND DYNAMICAL SYSTEMS

1998 ◽  
Vol 29 (2) ◽  
pp. 101-107
Author(s):  
R. K. SINGH ◽  
BHOPINDER SINGH
Keyword(s):  
Hausdorff Space ◽  
Weighted Space ◽  
Composition Operators ◽  
Continuous Functions ◽  
Weighted Composition Operators ◽  
Linear Dynamical System ◽  
Completely Regular ◽  
Weighted Composition ◽  
Locally Convex

Let $X$ be a completely regular Hausdorff space, $E$ a Hausdorff locally convex topo­logical vector space, and $V$ a system of weights on $X$. Denote by $CV_b(X, E)$ ($CV_o(X, E)$) the weighted space of all continuous functions $f : X \to E$ such that $vf (X)$ is bounded in $E$ (respectively, $vf$ vanishes at infinity on $X$) for all $v \in V$. In this paper, we give an improved characterization of weighted composition operators on $CV_b(X, E)$ and present a linear dynamical system induced by composition operators on the metrizable weighted space $CV_o(\mathbb{R}, E)$.

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