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 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.

Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

1999 ◽  
Vol 42 (2) ◽  
pp. 139-148 ◽  
Author(s):  
José Bonet ◽  
Paweł Dománski ◽  
Mikael Lindström
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Point Evaluation ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

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