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Spectra of composition operators on algebras of analytic functions on Banach spaces

Published online by Cambridge University Press:  13 March 2009

P. Galindo ,
T. W. Gamelin  and
Mikael Lindström
P. Galindo
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjasot, Valencia, Spain (galindo@uv.es)
T. W. Gamelin
Affiliation:
Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555, USA (twg@math.ucla.edu)
Mikael Lindström
Affiliation:
Department of Mathematical Sciences, University of Oulu, 90014 Oulu, Finland (mikael.lindstrom@oulu.fi).
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Abstract

Let E be a Banach space, with unit ball BE. We study the spectrum and the essential spectrum of a composition operator on H∞(BE) determined by an analytic symbol with a fixed point in BE. We relate the spectrum of the composition operator to that of the derivative of the symbol at the fixed point. We extend a theorem of Zheng to the context of analytic symbols on the open unit ball of a Hilbert space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 1 , February 2009 , pp. 107 - 121
Copyright
Copyright © Royal Society of Edinburgh 2009

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