scholarly journals Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces

2016 ◽  
pp. 1-18
Author(s):  
Ted Eklund ◽  
Mikael Lindström ◽  
Paweł Mleczko
Keyword(s):  
Spectral Properties ◽  
Composition Operators ◽  
Weighted Composition Operators ◽  
Dirichlet Spaces ◽  
Weighted Composition

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

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].

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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