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

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.

Authors:

• M. H. M. Rashid

Keywords:

• Weyl’s theorem
• Weyl spectrum
• polaroid operators
• property (gm)
• property (m).

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