Similarity, quasisimilarity, and operator factorizations
Raúl E. Curto, Lawrence A. Fialkow · Transactions of the American Mathematical Society · 1989
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 + {U_ + } , we obtain a one-parameter family of nonhyponormal, noncontractive, shift-like operators in the similarity orbit of U + {U_ + } . We also obtain new characterizations of quasisimilarity and similarity in terms of invariant operator ranges, and conditions for spectral and essential spectral inclusions.