Subnormal tuples quasi-similar to the Szegö tuple
It is well known that a cyclic subnormal n-tuple of commuting operators can be represented unitarily as the multiplications with the complex coordinates \(M_ z=(M_{z_ 1},...,M_{z_ n})\) on \(P^ 2(\mu)\). Here \(P^ 2(\mu)\) denotes the closure of polynomials in \(L^ 2(\mu)\), where \(\mu\) is a positive Borel measure, compactly supported on \({\mathbb{C}}^ n.\) By means of that model and using an approximation result of the analytic function theory in the unit ball B of \({\mathbb{C}}^ n\), the author characterizes those subnormal n-tuple which are quasisimilar to \(M_ z\) on \(P^ 2(\mu)\), \(\mu\) being a measure supported on \(\partial B\). In particular, for \(\mu\) \(=\) surface area measure on \(\partial B\), this result describes the quasi-similarity orbit of the Szegö n-tuple of subnormal operators.
cyclic subnormal n-tuple of commuting operators
scientific article; zbMATH DE number 4107494