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

 

Similarity, quasisimilarity, and operator factorizations


Authors: Raúl E. Curto and Lawrence A. Fialkow
Journal: Trans. Amer. Math. Soc. 314 (1989), 225-254
MSC: Primary 47A05; Secondary 47A10, 47A30, 47A53, 47A62, 47B37
MathSciNet review: 962277
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Abstract: We introduce and illustrate an operator factorization technique to study similarity and quasisimilarity of Hilbert space operators. The technique allows one to generate, in a systematic way, families of "test" operators, and to check for similarity and quasisimilarity with a given model. In the case of the unilateral shift $ {U_ + }$, we obtain a one-parameter family of nonhyponormal, noncontractive, shift-like operators in the similarity orbit of $ {U_ + }$. We also obtain new characterizations of quasisimilarity and similarity in terms of invariant operator ranges, and conditions for spectral and essential spectral inclusions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0962277-3
PII: S 0002-9947(1989)0962277-3
Keywords: Quasisimilarity, similarity, unilateral shift, operator factorizations, nilpotents, invariant operator ranges
Article copyright: © Copyright 1989 American Mathematical Society