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

2019/11/22 by Yu‐Xia Liang, Liang, Yuxia, J. R. Partington +1 · 1 citation
Mathematics · #46E22 #47A15 #47B38 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.1911.10072

openalex publication_date 2019/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Perturbations of Toeplitz operators on vector-valued Hardy spaces

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• Backward Shift Invariant Subspaces in Reproducing Kernel Hilbert Spaces