Similarity, quasisimilarity, and operator factorizations

Curto, Raúl E.; Fialkow, Lawrence A.

doi:10.1090/S0002-9947-1989-0962277-3

Similarity, quasisimilarity, and operator factorizations
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by Raúl E. Curto and Lawrence A. Fialkow PDF

Trans. Amer. Math. Soc. 314 (1989), 225-254 Request permission

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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