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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Iterates of an absolutely continuous operator


Author: P. Ghatage
Journal: Proc. Amer. Math. Soc. 49 (1975), 203-204
MSC: Primary 47A65
MathSciNet review: 0361871
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Abstract: It is proved that the powers of an absolutely continuous polynomially bounded operator, the intersection of whose spectrum with the circle has zero measure, go to zero strongly. From this we deduce a simple treatment of the Nagy-Foiaş result on completely nonunitary contractions.


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

  • [1] Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. MR 0133008 (24 #A2844)
  • [2] B. Sz.-Nagy and C. Foiaş, Analyse harmonique des opérateurs de l'espace de Hilbert, Akad. Kiadó, Budapest, 1967; English transl., North-Holland, Amsterdam; American Elsevier, New York, 1970. MR 43 #947.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0361871-6
PII: S 0002-9939(1975)0361871-6
Keywords: Polynomially bounded, absolutely continuous, strong convergence
Article copyright: © Copyright 1975 American Mathematical Society