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Composition operators on some Möbius invariant Banach spaces

Published online by Cambridge University Press:  17 April 2009

Shamil Makhmutov  and
Maria Tjani
Shamil Makhmutov
Affiliation:
Department of Mathematics, Ufa State Aviation Technical University, Ufa 450000, Russia, e-mail: makhm@ugatu.ac.ru
Maria Tjani
Affiliation:
Department of Mathematical Sciences, 301 Science Engineering Building, University of Arkansas, Fayetteville AR 72701, United States of America, e-mail: mtjani@comp.uark.edu
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Abstract

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We characterise the compact composition operators from any Mobius invariant Banach space to VMOA, the space of holomorphic functions on the unit disk U that have vanishing mean oscillation. We use this to obtain a characterisation of the compact composition operators from the Bloch space to VMOA. Finally, we study some properties of hyperbolic VMOA functions. We show that a function is hyperbolic VMOA if and only if it is the symbol of a compact composition operator from the Bloch space to VMOA.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 1 - 19
Copyright
Copyright © Australian Mathematical Society 2000

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