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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 314 (1989), 225-254
- MSC: Primary 47A05; Secondary 47A10, 47A30, 47A53, 47A62, 47B37
- DOI: https://doi.org/10.1090/S0002-9947-1989-0962277-3
- MathSciNet review: 962277