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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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On Toeplitz operators which are contractions
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by Robert Goor PDF
Proc. Amer. Math. Soc. 34 (1972), 191-192 Request permission

Abstract:

We prove that a Toeplitz contraction ${T_\phi }$ is completely nonunitary if $\phi$ is not a constant. As an application, it is noted that for such ${T_\phi }$, a functional calculus can be defined for all functions u in ${H^\infty }$ of the unit disk.
References
  • Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
    • B. Sz.-Nagy and C. Foiaş, Analyse harmonique des opérateurs de l’espace de Hilbert, Masson, Paris; Akad. Kiadó, Budapest, 1967. MR 37 #778.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 191-192
  • MSC: Primary 47B35
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0293443-3
  • MathSciNet review: 0293443