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Inner Functions and Isometries

Published online by Cambridge University Press:  20 November 2018

Paul S. Muhly
Paul S. Muhly*
Affiliation:
The University of Iowa, Iowa City, Iowa 52242
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Our objective in this note is to prove a theorem about the spectral behavior of certain multiplication operators. It was motivated by and yields an extension of part of a theorem of Lumer [3] concerning the possibility of imbedding the classical Hardy spaces in abstract ones.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 3 , August 1975 , pp. 383 - 385
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Douglas, R. G., On the hyperinvariant subspacesfor isometries, Math. Z. 107 (1968), 297-300.Google Scholar
2. Halmos, P. R., A Hilbert space Problem Book, Van Nostrand, Princeton (1967).Google Scholar
3. Lumer, G., H∞ and the imbedding of the classical Hp spaces in arbitrary ones, Function Algebras, Scott Foresman; Chicago (1966).Google Scholar
4. Sz.-Nagy, B. and Foiaç, C., Analyse harmonique des opérateurs de l'espace de Hilbert, Akademiai Kiado, Budapest, 1967.Google Scholar