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
DOI:
https://doi.org/10.1090/S0002-9939-04-07474-X
Published electronically:
May 21, 2004
MathSciNet review:
2073306
Full-text PDF Free Access
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
