M. H. M. Rashid
Stability of Property (gm) under Perturbation and Spectral Properties Type Weyl Theorems
34 - 39
2019
13
2
International Journal of Physical and Mathematical Sciences
https://publications.waset.org/pdf/10010032
https://publications.waset.org/vol/146
World Academy of Science, Engineering and Technology
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 quasinilpotent operators, or more generally by algebraic operators
commuting with T.
Open Science Index 146, 2019