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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).


References [Enhancements On Off] (What's this?)

  • [1] E. Berkson and H. Porta, The group of isometries on Hardy spaces of the $ n$-ball and the polydisc, Glasgow Math. J. (to appear). MR 582130 (81m:32006)
  • [2] P. Duren, Theory of $ {H^p}$ spaces, Pure and Appl. Math., Vol. 38, Academic Press, New York and London, 1970. MR 0268655 (42:3552)
  • [3] G. M. Goluzin, Geometric theory of functions of a complex variable, Transl. Math. Monos., Vol. 26, Amer. Math. Soc., Providence, R.I., 1969. MR 0247039 (40:308)

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Additional Information

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

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