Finite rank perturbations of concentrations (Q1566818)

Let \(T\) be a contraction on an infinite-dimensional complex Hilbert space with finite-dimensional defect spaces \(D_T\) and \(D_{T^*}\). Assume that \(T^{*n}x\to 0\) for any \(x\in H\). \(T\) is then said to be of class \(C_0\). The author studies finite rank perturbations of contractions of class \(C_0\). It is shown that the completely non-unitary part of such a perturbation is also of class \(C_{\cdot 0}\) while the unitary part is singular. In the case of non-equel defect indices of the original contraction, the perturbation has almost no unitary part.