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Transactions of the American Mathematical Society

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

 

 

Subnormal operators quasisimilar to an isometry


Author: William W. Hastings
Journal: Trans. Amer. Math. Soc. 256 (1979), 145-161
MSC: Primary 47B20
DOI: https://doi.org/10.1090/S0002-9947-1979-0546912-3
MathSciNet review: 546912
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Abstract: Let $ V = {V_0} \oplus {V_1}$ be an isometry, where $ {V_0}$ is unitary and $ {V_1}$ is a unilateral shift of finite multiplicity n. Let $ S = {S_0} \oplus {S_1}$ be a subnormal operator where $ {S_0} \oplus {S_1}$ is the normal decomposition of S into a normal operator $ {S_0}$ and a completely nonnormal operator $ {S_1}$. It is shown that S is quasisimilar to V if and only if $ {S_0}$ is unitarily equivalent to $ {V_0}$ and $ {S_1}$ is quasisimilar to $ {V_1}$. To prove this, a standard representation is developed for n-cyclic subnormal operators. Using this representation, the class of subnormal operators which are quasisimilar to $ {V_1}$ is completely characterized.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0546912-3
Keywords: Subnormal operator, isometry, quasisimilar, normal decomposition, unilateral shift, dominant operator
Article copyright: © Copyright 1979 American Mathematical Society