A note on property (gaR) and perturbations

  • A. Chen
  • J. L. Shen

Abstract

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.
Published
25.07.2017
How to Cite
ChenA., and ShenJ. L. “A Note on Property (gaR) and Perturbations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 7, July 2017, pp. 974-83, http://umj.imath.kiev.ua/index.php/umj/article/view/1750.
Section
Research articles