Vasyunin, V. I.; Makarov, N. G. On quasi-similarity of model contractions with nonequal defects. (Russian. English summary) Zbl 0606.47015 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 149, 24-37 (1986). Let \(T_{\theta}\) and \(T_{\phi}\) be \(C_{10}\) contractions with characteristic functions \(\theta \in H^{\infty}({\mathbb{C}}^ n\to {\mathbb{C}}^{n+1})\) and \(\phi \in H^{\infty}({\mathbb{C}}^ m\to {\mathbb{C}}^{m+1})\). The main \(result:\) T\({}_{\theta}\) and \(T_{\phi}\) are quasi-similar iff \[ \{\det (f,\theta)^ i:f\in H^ 2_ n\}=\{\det (g,\phi)^ i:g\in H^ 2_ m\}. \] The paper contains an analysis of this condition. Some examples are given. Cited in 1 ReviewCited in 2 Documents MSC: 47A45 Canonical models for contractions and nonselfadjoint linear operators Keywords:C\({}_{10}\) contractions; quasi-similar PDFBibTeX XMLCite \textit{V. I. Vasyunin} and \textit{N. G. Makarov}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 149, 24--37 (1986; Zbl 0606.47015) Full Text: EuDML