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On quasi-similarity of model contractions with nonequal defects. (Russian. English summary) Zbl 0606.47015

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.

MSC:

47A45 Canonical models for contractions and nonselfadjoint linear operators
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