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arXiv · 2610.29710

Property (R) with its stability for analytic functional system and under compact perturbations

Sinan Qiu·Lining Jiang·Xiaomin Wei
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Abstract

Let $\mathcal{F}_T$ be the analytic functional system generated by a linear bounded operator $T$ on an infinite dimensional complex Hilbert space. This paper characterizes the stability of property (R), a variant of Weyl's theorem, for $\mathcal{F}_T$ and under compact perturbations in terms of the spectrum on consistency in Weyl. In particular, the stability of property (R) under compact perturbations is shown to imply the (R)-stability of $\mathcal{F}_T$.

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Sinan Qiu, Lining Jiang, Xiaomin Wei. 2026-10-21. Property (R) with its stability for analytic functional system and under compact perturbations. https://arxiv.org/abs/2610.29710

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