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Proceedings of the American Mathematical Society

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



On Toeplitz operators which are contractions

Author: Robert Goor
Journal: Proc. Amer. Math. Soc. 34 (1972), 191-192
MSC: Primary 47B35
MathSciNet review: 0293443
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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 [Enhancements On Off] (What's this?)

  • [1] Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
  • [2] 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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Keywords: Toeplitz operator, contraction, completely nonunitary, reducing subspace, Beurling theorem, F. and M. Riesz theorem
Article copyright: © Copyright 1972 American Mathematical Society