Representing kernels of perturbations of Toeplitz operators by backward shift-invariant subspaces (Q2196521)

Invariant subspaces are very important object in operator theory and its well known that the kernel of a Toeplitz operator is nearly invariant under the backward shift \(S^*\). Theorem 2.3, Theorem 2.4 and Theorem 2.6 show that the kernels of finite rank perturbations of Toeplitz operators are nearly \(S^*\) invariant with finite defect. The result of the mentioned theorems enables the authors to apply a recent theorem by Chalendar-Gallardo-Partington to show the kernel in terms of backward shift-invariant subspaces as was shown in corollaries 3.3, 3.4, 3.5, 3.6, 3.8.