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Extended Weyl theorems and perturbations


In this paper we study the properties $( \rm{gaw}), (aw), ( \rm{gab})$ and $(ab)$, a variant of Weyl's type theorems introduced by Berkani. We established for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which the properties $(\rm{gaw}), (aw), ( \rm{gab})$ and $(ab)$ hold. Among other things, we study the stability of the properties $( \rm{gaw}), (aw), ( \rm{gab})$ and $(ab)$ for a polaroid operator $T$ acting on a Banach space, under perturbations by finite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with $T$.

Key words: Generalized Weyl’s theorem, generalized a-Weyl’s theorem, property (gb), property (gw), polaroid operators, perturbation theory.

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TitleExtended Weyl theorems and perturbations
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 80-96
MathSciNet   MR3088321
zbMATH 1289.47027
Milestones  Received 26/08/2012
CopyrightThe Author(s) 2013 (CC BY-SA)

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M. H. M. Rashid
Department of Mathematics and Statistics, Faculty of Science, P.O.Box(7), Mu'tah University, l-karak-Jordan 

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M. H. M. Rashid, Extended Weyl theorems and perturbations, Methods Funct. Anal. Topology 19 (2013), no. 1, 80-96.


@article {MFAT664,
    AUTHOR = {Rashid, M. H. M.},
     TITLE = {Extended Weyl theorems and perturbations},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {80-96},
      ISSN = {1029-3531},
  MRNUMBER = {MR3088321},
 ZBLNUMBER = {1289.47027},
       URL = {},

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