scholarly journals Fredholm Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions of TypeH∞

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
M. Carmen Gómez-Collado ◽  
David Jornet
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Unit Disc ◽  
Composition Operators ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disc ◽  
Weighted Composition ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

We study Fredholm (weighted) composition operators between general weighted Banach spaces of analytic functions on the open unit disc with sup-norms.

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.

scholarly journals BELLWETHERS FOR BOUNDEDNESS OF COMPOSITION OPERATORS ON WEIGHTED BANACH SPACES OF ANALYTIC FUNCTIONS

2009 ◽  
Vol 86 (3) ◽  
pp. 305-314 ◽  
Author(s):  
PAUL S. BOURDON
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Open Unit ◽  
Sufficient Condition ◽  
Angular Derivative ◽  
Open Unit Disc ◽  
Weighted Banach Space ◽  
Growth Space ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractLet 𝔻 be the open unit disc, let v:𝔻→(0,∞) be a typical weight, and let Hv∞ be the corresponding weighted Banach space consisting of analytic functions f on 𝔻 such that $\|f\|_v:=\sup _{z\in \mathbb {D}}v(z)\lvert f(z)\rvert \less \infty $. We call Hv∞ a typical-growth space. For ϕ a holomorphic self-map of 𝔻, let Cφ denote the composition operator induced by ϕ. We say that Cφ is a bellwether for boundedness of composition operators on typical-growth spaces if for each typical weight v, Cφ acts boundedly on Hv∞ only if all composition operators act boundedly on Hv∞. We show that a sufficient condition for Cφ to be a bellwether for boundedness is that ϕ have an angular derivative of modulus less than 1 at a point on ∂𝔻. We raise the question of whether this angular-derivative condition is also necessary for Cφ to be a bellwether for boundedness.

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