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arXiv · 2404.06067

Kernels of Perturbed Hankel Operators

Arup Chattopadhyay·Supratim Jana
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Abstract

In the classical Hardy space $H^2(\mathbb{D})$, it is well-known that the kernel of the Hankel operator is invariant under the action of shift operator S and sometimes nearly invariant under the action of backward shift operator $S^{*}$. It appears in this paper that kernels of finite rank perturbations of Hankel operators are almost shift invariant as well as nearly $S^*$- invariant with finite defect. This allows us to obtain a structure of the kernel in several important cases by applying a recent theorem due to Chalendar, Gallardo, and Partington.

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Arup Chattopadhyay, Supratim Jana. 2024-04-09. Kernels of Perturbed Hankel Operators. https://arxiv.org/abs/2404.06067

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