Proceedings of the American Mathematical Society

Author(s): C-H. Chu; R. V. Hügli; M. Mackey
Journal: Proc. Amer. Math. Soc. 132 (2004), 3305-3308.
MSC (2000): Primary 47B38, 46J15, 46G20, 32A10
Posted: May 21, 2004
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Abstract: Let $H^\infty(B)$ 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 $H^\infty(B)$ . This answers a conjecture of Aron, Galindo and Lindström.

1.: R. ARON, P. GALINDO AND M. LINDSTRÖM, Connected components in the space of composition operators, Integr. Equ. Oper. Theory, 45 (2003) 1-14. MR 2003m:47041
2.: E. BISHOP AND R. R. PHELPS, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc., 67 (1961) 97-98.MR 23:A503
3.: F. F. BONSALL AND J. DUNCAN, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, Vol. 2, London Math. Soc. Lect. Note Ser., Cambridge Univ. Press (1971) Cambridge.MR 44:5779
4.: S. DINEEN, The Schwarz Lemma, Oxford Univ. Press (1989) Oxford.MR 91f:46064
5.: P. GALINDO AND M. LINDSTRÖM, Factorization of homomorphisms through $H^\infty(D)$ , J. Math. Anal. Appl. 280 (2003) 375-386.
6.: B. MACCLUER, S. OHNO AND R. ZHAO, Topological structure of the space of composition operators on ${H}\sp \infty$ , Integr. Equ. Oper. Theory, 40 (2001) 481-494. MR 2002d:47039
7.: M. MACKEY AND P. MELLON, A Schwarz lemma and composition operators, Integr. Equ. Oper. Theory (to appear).

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B38, 46J15, 46G20, 32A10

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

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