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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Composition operators isolated in the uniform operator topology


Author: Earl Berkson
Journal: Proc. Amer. Math. Soc. 81 (1981), 230-232
MSC: Primary 47B38; Secondary 30D55
DOI: https://doi.org/10.1090/S0002-9939-1981-0593463-0
MathSciNet review: 593463
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Abstract: It is is shown that $ \phi $ is an analytic map of the disc $ \left\vert z \right\vert < 1$ into itself such that $ \phi $ has radial limits of modulus 1 on a set of positive measure, then for $ 1 \leqslant p < \infty $ the corresponding composition operator on $ {H^p}$ is isolated in the topological space of composition operators on $ {H^p}$ (with the uniform operator topology).


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DOI: https://doi.org/10.1090/S0002-9939-1981-0593463-0
Keywords: Composition operator, $ {H^p}$
Article copyright: © Copyright 1981 American Mathematical Society