On Toeplitz operators which are contractions
Author:
Robert Goor
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
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Abstract | References | Similar Articles | Additional Information
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.
- 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
Keywords:
Toeplitz operator,
contraction,
completely nonunitary,
reducing subspace,
Beurling theorem,
F. and M. Riesz theorem
Article copyright:
© Copyright 1972
American Mathematical Society
