科研之友
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摘要
We introduce a new property (gaR) extending the property (R) considered by Aiena. We study the property (gaR) in connection with the 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.
