scholarly journals Spectra of some invertible weighted composition operators on Hardy and weighted Bergman spaces in the unit ball

2016 ◽  
Vol 41 ◽  
pp. 177-198 ◽  
Author(s):  
Yong-Xin Gao ◽  
Ze-Hua Zhou
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Weighted Composition Operators ◽  
Weighted Composition

Weighted composition operators on weighted Bergman spaces induced by doubling weights

2020 ◽  
Vol 126 (3) ◽  
pp. 519-539
Author(s):  
Juntao Du ◽  
Songxiao Li ◽  
Yecheng Shi
Keyword(s):  
Composition Operators ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Weighted Bergman Spaces ◽  
Weighted Composition Operators ◽  
Schatten Class ◽  
Doubling Weight ◽  
Doubling Weights ◽  
Type Spaces ◽  
Weighted Composition

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi $ on Bergman type spaces $A_\omega ^p $ induced by a doubling weight ω. Let $X=\{u\in H(\mathbb{D} ): uC_\varphi \colon A_\omega ^p\to A_\omega ^p\ \text {is bounded}\}$. For some regular weights ω, we obtain that $X=H^\infty $ if and only if ϕ is a finite Blaschke product.

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