## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Property $(\rm{gw})$ and perturbations

M. H. M. Rashid

#### 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 4 (2011), 635-654.

Dates
First available in Project Euclid: 8 November 2011

https://projecteuclid.org/euclid.bbms/1320763127

Digital Object Identifier
doi:10.36045/bbms/1320763127

Mathematical Reviews number (MathSciNet)
MR2907609

Zentralblatt MATH identifier
1221.47011

#### Citation

Rashid, M. H. M. Property $(\rm{gw})$ and perturbations. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 4, 635--654. doi:10.36045/bbms/1320763127. https://projecteuclid.org/euclid.bbms/1320763127