scholarly journals Normal weighted composition operators on weighted Dirichlet spaces

2015 ◽  
Vol 423 (1) ◽  
pp. 758-769 ◽  
Author(s):  
Lu Li ◽  
Yukihide Nakada ◽  
Douglas Nestor ◽  
Wendy Shang ◽  
Rachel Weir
Keyword(s):  
Composition Operators ◽  
Weighted Composition Operators ◽  
Dirichlet Spaces ◽  
Weighted Dirichlet Spaces ◽  
Weighted Composition

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

2019 ◽  
Vol 31 (01) ◽  
pp. 2050006
Author(s):  
Xiaohe Hu ◽  
Zicong Yang ◽  
Zehua Zhou
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Necessary Condition ◽  
Weighted Composition Operators ◽  
Dirichlet Spaces ◽  
Weighted Composition ◽  
Complex Symmetric ◽  
Sufficient And Necessary Condition

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].

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