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

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 ®, 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 ® under compact perturbations is shown to imply the ®-stability of ${\mathcal{F}}_T$.