scholarly journals Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions

2021 ◽  
Vol 280 (3) ◽  
pp. 108834
Author(s):  
Pascal Lefèvre ◽  
Daniel Li ◽  
Hervé Queffélec ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Singular Numbers ◽  
Spaces Of Analytic Functions

scholarly journals Weighted Composition Operators and Supercyclicity Criterion

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Bahmann Yousefi ◽  
Javad Izadi
Keyword(s):  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Equivalent Condition ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Supercyclicity Criterion ◽  
Spaces Of Analytic Functions

We consider an equivalent condition to the property of Supercyclicity Criterion, and then we investigate this property for the adjoint of weighted composition operators acting on Hilbert spaces of analytic functions.

Generalized Composition Operators on Weighted Hilbert Spaces of Analytic Functions

2017 ◽  
Vol 10 ◽  
pp. 1-13 ◽  
Author(s):  
Waleed Al-Rawashdeh
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Carleson Measures ◽  
Open Unit ◽  
Open Unit Disk ◽  
Admissible Weight ◽  
Spaces Of Analytic Functions

Letφbe an analytic self-map of the open unit disk D andgbe an analytic function on D. The generalized composition operator induced by the mapsgandφis defined by the integral operatorI(g,φ)f(z) =∫0zf′(φ(ς))g(ς)dς. Given an admissible weightω, the weighted Hilbert spaceHωconsists of all analytic functionsfsuch that ∥f∥2Hω= |f(0)|2+∫D|f′(z)|2ω(z)dA(z) is finite. In this paper, we characterize the boundedness and compactness of the generalized composition operators on the spaceHωusing theω-Carleson measures. Moreover, we give a lower bound for the essential norm of these operators.

scholarly journals Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Zoryana Mozhyrovska ◽  
Andriy V. Zagorodnyuk
Keyword(s):  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Translation Operator ◽  
Translation Operators ◽  
Spaces Of Analytic Functions

We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic.

scholarly journals Simply connected topological spaces of weighted composition operators

2020 ◽  
Vol 18 (1) ◽  
pp. 1440-1450
Author(s):  
Cezhong Tong ◽  
Zhan Zhang ◽  
Biao Xu
Keyword(s):  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Topological Spaces ◽  
Weighted Composition Operators ◽  
Open Ball ◽  
Weighted Composition ◽  
Simply Connected ◽  
Spaces Of Analytic Functions

Abstract In this paper, we prove that the topological spaces of nonzero weighted composition operators acting on some Hilbert spaces of analytic functions on the unit open ball are simply connected.

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