scholarly journals Generalized Essential Norm of Weighted Composition Operators on some Uniform Algebras of Analytic Functions

2009 ◽  
Vol 63 (4) ◽  
pp. 557-569 ◽  
Author(s):  
Pascal Lefèvre
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Uniform Algebras ◽  
Weighted Composition

Boundary vs. interior conditions associated with weighted composition operators

2014 ◽  
Vol 12 (5) ◽  
Author(s):  
Kei Izuchi ◽  
Yuko Izuchi ◽  
Shûichi Ohno
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weight Functions ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Weighted Composition ◽  
The Difference ◽  
Harmonic And Analytic Functions

AbstractAssociated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk $$\mathbb{D}$$, we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior $$\mathbb{D}$$ and on the boundary $$\partial \mathbb{D}$$ respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.

scholarly journals Weighted composition operators in weighted Banach spaces of analytic functions

2000 ◽  
Vol 69 (1) ◽  
pp. 41-60 ◽  
Author(s):  
M. D. Contreras ◽  
A. G. Hernandez-Diaz
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Type Spaces ◽  
Weighted Composition ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractWe characterize the boundedness and compactness of weighted composition operators between weighted Banach spaces of analytic functions and . we estimate the essential norm of a weighted composition operator and compute it for those Banach spaces which are isomorphic to c0. We also show that, when such an operator is not compact, it is an isomorphism on a subspace isomorphic to c0 or l∞. Finally, we apply these results to study composition operators between Bloch type spaces and little Bloch type spaces.

Essential norm of weighted composition operators

Analysis ◽  
2018 ◽  
Vol 38 (3) ◽  
pp. 145-154
Author(s):  
Kuldip Raj ◽  
Charu Sharma
Keyword(s):  
Composition Operators ◽  
Essential Norm ◽  
Function Spaces ◽  
Weighted Composition Operators ◽  
Closed Range ◽  
Weighted Composition

Abstract In the present paper we characterize the compact, invertible, Fredholm and closed range weighted composition operators on Cesàro function spaces. We also make an effort to compute the essential norm of weighted composition operators.

scholarly journals Weighted composition operators between weak spaces of vector-valued analytic functions

Analysis ◽  
2017 ◽  
Vol 37 (1) ◽  
Author(s):  
Mostafa Hassanlou ◽  
Jussi Laitila ◽  
Hamid Vaezi
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Vector Valued

AbstractWe consider weighted composition operators

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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