CUBO A Mathematical Journal Vol.12, N° 02, (19–27). June 2010

 

Differences of weighted composition operators between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces

 

Elke Wolf

Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany. email: lichte@math.uni-paderborn.de

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ABSTRACT

We consider analytic self-maps ø1,ø 2 of the open unit disk as well as analytic mapsψ 1, ψ2. These maps induce differences of weighted composition operators acting between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces. In this article we give necessary and sufficient conditions for such a difference to be bounded resp. compact.

Key words and phrases: weighted composition operators, weighted Bloch type spaces, weighted Banach spaces of holomorphic functions.

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RESUMEN

Nosotros consideramos auto aplicaciones ø1,ø 2 del disco unitario abierto bien como aplicaciones analíticas ψ1, ψ2. Estas aplicaciones inducen diferencias de compición de operadores con peso actuando entre espacios de Banach pesados de funciones holomorfas y espacios de tipo Bloch con peso. En este artículo damos condiciones necesarias y suficientes para que tal diferencia sea acotada, respectivamente, compacta.

Math. Subj. Class. 2000: 47B33, 47B38.

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Received: October 2008.

Revised: February 2009.