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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Hyponormal operators quasisimilar to an isometry

Author: Pei Yuan Wu
Journal: Trans. Amer. Math. Soc. 291 (1985), 229-239
MSC: Primary 47B20; Secondary 47A45
MathSciNet review: 797056
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Abstract: An expression for the multiplicity of an arbitrary contraction is presented. It is in terms of the isometries which can be densely intertwined to the given contraction. This is then used to obtain a generalization of a result of Sz.-Nagy and Foiaş concerning the existence of a $ C{._0}$ contraction which is a quasiaffine transform of a contraction. We then consider the problem when a hyponormal operator is quasisimilar to an isometry or, more generally, when two hyponormal contractions are quasisimilar to each other. Our main results in this respect generalize previous ones obtained by Hastings and the author. For quasinormal and certain subnormal operators, quasisimilarity or similarity to an isometry may even imply unitary equivalence.

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PII: S 0002-9947(1985)0797056-X
Keywords: Contraction, unilateral shift, contraction of analytic type, isometry, quasisimilarity, multiplicity, hyponormal operator, quasinormal operator, Toeplitz operator
Article copyright: © Copyright 1985 American Mathematical Society