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 | References | Similar Articles | Additional Information

Abstract: Let be the Banach algebra of bounded holomorphic functions on the open unit ball of a Banach space. We show that the identity operator is an isolated point in the space of composition operators on . 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:
https://doi.org/10.1090/S0002-9939-04-07474-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