Bulletin of the Belgian Mathematical Society - Simon Stevin

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

M. H. M. Rashid

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1320763127

Digital Object Identifier
doi:10.36045/bbms/1320763127

Mathematical Reviews number (MathSciNet)
MR2907609

Zentralblatt MATH identifier
1221.47011

Subjects
Primary: 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
Secondary: 47A10: Spectrum, resolvent 47A11: Local spectral properties 47A20: Dilations, extensions, compressions

Keywords
Generalized Weyl's theorem Generalized $a$-Weyl's theorem Property $(\rm{gw})$ Polaroid operators Perturbation Theory

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


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