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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Contraction operators quasisimilar to a unilateral shift

Author: V. T. Alexander
Journal: Trans. Amer. Math. Soc. 283 (1984), 697-703
MSC: Primary 47A45
MathSciNet review: 737893
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Abstract: Let $ {U_n}$ denote the unilaterial shift of finite multiplicity $ n$. It is shown that a contraction operator $ T$ is quasisimilar to $ {U_n}$ if and only if $ T$ is of Class $ {C_1}$., the canonical isometry $ V$ associated with $ T$ is pure and $ T$ is $ n$-cyclic with analytically independent vectors. For this, the notions of operators of analytic type and analytic independence of vectors are introduced. A characterization of the cyclic vectors of the Backward Shift is also presented.

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Keywords: Contraction, unilateral shift, operator of analytic type, isometry, quasisimilarity
Article copyright: © Copyright 1984 American Mathematical Society