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

 

Isolated points and essential components of composition operators on $H^\infty$


Authors: Takuya Hosokawa, Keiji Izuchi and Dechao Zheng
Journal: Proc. Amer. Math. Soc. 130 (2002), 1765-1773
MSC (2000): Primary 47B33, 47B38
Published electronically: October 24, 2001
MathSciNet review: 1887024
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Abstract: We consider the topological space of all composition operators on the Banach algebra of bounded analytic functions on the unit disk. We obtain a function theoretic characterization of isolated points and show that each isolated composition operator is essentially isolated.


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Additional Information

Takuya Hosokawa
Affiliation: Department of Mathematics, Niigata University, Niigata, 950-2181, Japan

Keiji Izuchi
Affiliation: Department of Mathematics, Niigata University, Niigata, 950-2181, Japan
Email: izuchi@math.sc.niigata-u.ac.jp

Dechao Zheng
Affiliation: Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240
Email: zheng@math.vanderbilt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06233-5
PII: S 0002-9939(01)06233-5
Keywords: Composition operators, asymptotically interpolating sequences
Received by editor(s): September 6, 2000
Received by editor(s) in revised form: December 15, 2000
Published electronically: October 24, 2001
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society