Abstract
The property $(\rm{gw})$ is a variant of generalized Weyl's theorem, for a bounded operator $T$ acting on a Banach space. In this note we consider the preservation of property $(\rm{gw})$ under a finite rank perturbation commuting with $T$, whenever $T$ is isoloid, polaroid, or $T$ has analytical core $K(\lamda_0 I -T ) = \set{0}$ for some $\lamda_0\in\mathbb{C}$. The preservation of property $(\rm{gw})$ is also studied under commuting nilpotent or under algebraic perturbations. The theory is exemplified in the case of some special classes of operators.
Citation
M. H. M. Rashid. "Property $(\rm{gw})$ and perturbations." Bull. Belg. Math. Soc. Simon Stevin 18 (4) 635 - 654, november 2011. https://doi.org/10.36045/bbms/1320763127
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