A note on property (gaR) and perturbations - Chen, A.; Shen, J. L. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We introduce a new property (gaR) extending the property (R) considered by Aiena. We study the property (gaR) in connection with Weyl type theorems and establish sufficient and necessary conditions under which the property (gaR) holds. In addition, we also study the stability of the property (gaR) under perturbations by finite-dimensional operators, by nilpotent operators, by quasinilpotent operators, and by algebraic operators commuting with T. The classes of operators are considered as illustrating examples.