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Weighted composition operators in weighted Banach spaces of analytic functions

Part of: Linear function spaces and their duals Entire and meromorphic functions, and related topics Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

M. D. Contreras  and
A. G. Hernandez-Diaz
A. G. Hernandez-Diaz
Affiliation:
Departmento de Matem´tica Aplicada II Escuela Superior de Ingenieros Universidad de SevillaCamino de los Descubrimientos, s/n 41092, SevillaSpain e-mail: mcm@matinc.us.es e-mail: alfredo@matinc.us.es
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Abstract

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We 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.

MSC classification

Secondary: 47B38: Operators on function spaces (general) 30D45: Bloch functions, normal functions, normal families 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 1 , August 2000 , pp. 41 - 60
Copyright
Copyright © Australian Mathematical Society 2000

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