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It is well known that the kernel of a Toeplitz operator is nearly invariant under the backward shift $S^*$. This paper shows that kernels of finite-rank perturbations of Toeplitz operators… Click to show full abstract
It is well known that the kernel of a Toeplitz operator is nearly invariant under the backward shift $S^*$. This paper shows that kernels of finite-rank perturbations of Toeplitz operators are nearly $S^*$-invariant with finite defect. This enables us to apply a recent theorem by Chalendar--Gallardo--Partington to represent the kernel in terms of backward shift-invariant subspaces, which we identify in several important cases.
Keywords:
toeplitz operators;
backward shift;
perturbations toeplitz;
representing kernels;
shift invariant;
invariant subspaces
Journal Title: Integral Equations and Operator Theory
Year Published: 2020
Link to full text (if available)
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Journal Title: Integral Equations and Operator Theory
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!