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arXiv · 2107.05052

Invariant subspaces of analytic perturbations

Susmita Das·Jaydeb Sarkar
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Abstract

By analytic perturbations, we refer to shifts that are finite rank perturbations of the form $M_z + F$, where $M_z$ is the unilateral shift and $F$ is a finite rank operator on the Hardy space over the open unit disc. Here shift refers to the multiplication operator $M_z$ on some analytic reproducing kernel Hilbert space. In this paper, we first isolate a natural class of finite rank operators for which the corresponding perturbations are analytic, and then we present a complete classification of invariant subspaces of those analytic perturbations. We also exhibit some instructive examples and point out several distinctive properties (like cyclicity, essential normality, hyponormality, etc.) of analytic perturbations.

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Susmita Das, Jaydeb Sarkar. 2021-07-11. Invariant subspaces of analytic perturbations. https://arxiv.org/abs/2107.05052

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