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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The identity is isolated among composition operators


Authors: C-H. Chu, R. V. Hügli and M. Mackey
Journal: Proc. Amer. Math. Soc. 132 (2004), 3305-3308
MSC (2000): Primary 47B38, 46J15, 46G20, 32A10
Published electronically: May 21, 2004
MathSciNet review: 2073306
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Abstract: Let $H^\infty(B)$ be the Banach algebra of bounded holomorphic functions on the open unit ball $B$ of a Banach space. We show that the identity operator is an isolated point in the space of composition operators on $H^\infty(B)$. This answers a conjecture of Aron, Galindo and Lindström.


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Additional Information

C-H. Chu
Affiliation: School of Mathematical Sciences, Queen Mary College, University of London, London E1 4NS, England
Email: c.chu@qmul.ac.uk

R. V. Hügli
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: remo.huegli@stat.unibe.ch

M. Mackey
Affiliation: Department of Mathematics, University College, Dublin 4, Ireland
Email: michael.mackey@ucd.ie

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07474-X
PII: S 0002-9939(04)07474-X
Keywords: Composition operator, holomorphic function on Banach space, Carath\'eodory distance
Received by editor(s): May 7, 2003
Received by editor(s) in revised form: August 12, 2003
Published electronically: May 21, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society