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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectra of compact composition operators
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by James G. Caughran and Howard J. Schwartz PDF
Proc. Amer. Math. Soc. 51 (1975), 127-130 Request permission

Abstract:

Let $\phi$ be holomorphic and map the open unit disk into itself, and let ${C_\phi }:f \to f \circ \phi$ be the composition operator on ${H^2}$ generated by $\phi$. If ${C_\phi }$ is a compact operator then $(1)\phi ({z_0}) = {z_0}$ for some ${z_0} \epsilon D$; $(2)\sigma ({C_\phi }) = \{ \phi ’{({z_0})^n}:n = 0,1,2, \ldots \} \cup \{ 0\}$.
References
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 127-130
  • MSC: Primary 47B37; Secondary 30A18
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0377579-7
  • MathSciNet review: 0377579