Subnormal operators of finite type. II: Structure theorems
In connection with Xia's results for a pure (i.e., it has no normal part) subnormal operator (i.e., it has a normal extension) with finite rank self-commutator, which is called of finite type, the author gives, in this second paper, a complete structure result for subnormal operators of finite type, which corrects and strengthens Xia's formulation. Xia claimed that each subnormal operator of finite type is unitarily equivalent to the multiplicative operator by \(z\) on a weighted vector \(H^2\)-space over a ``quadrature Riemann surface'' (with a finite rank perturbation of the norm). Xia's formula is not accurate, because it would follow from it that every subnormal operator of finite type is simple but there is an example of a subnormal operator of finite type which is not necessarily simple. And the author explains how this formulation can be corrected.
scientific article; zbMATH DE number 1275455