a-Weyl's theorem and perturbations
Volume 173 / 2006
Studia Mathematica 173 (2006), 193-201 MSC: 47A53, 47A55. DOI: 10.4064/sm173-2-6
We study the stability of a-Weyl's theorem under perturbations by operators in some known classes. We establish in particular that if $T$ is a finite a-isoloid operator, then a-Weyl's theorem is transmitted from $T$ to $T+R$ for every Riesz operator $R$ commuting with $T$.