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arXiv · 2512.06967

On Quasinormality of compact perturbations of the isometries

Susmita Das
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Abstract

We study the compact perturbations of an isometry on a separable Hilbert space and provide a complete characterization of when they are quasinormal. Based on that, we present a complete classification for a rank-one perturbation of a unilateral shift of finite multiplicity to be quasinormal in the setting of the Hardy space. The result can also be generalized for a separable Hilbert space. As an application, we provide a complete characterization for quasinormality of a rank-one perturbation of the Hardy shift.

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Susmita Das. 2025-12-07. On Quasinormality of compact perturbations of the isometries. https://arxiv.org/abs/2512.06967

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