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Stability of Property (gm) under Perturbation and Spectral Properties Type Weyl Theorems

Authors: M. H. M. Rashid


A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl Spectrum, Polaroid operators, property (gm), Weyl’s theorem, property (m)

Digital Object Identifier (DOI):

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