Iterates of an absolutely continuous operator
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- by P. Ghatage PDF
- Proc. Amer. Math. Soc. 49 (1975), 203-204 Request permission
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
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008 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.
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 203-204
- MSC: Primary 47A65
- DOI: https://doi.org/10.1090/S0002-9939-1975-0361871-6
- MathSciNet review: 0361871