Abstract. Some classical perturbation results on Fredholm theory are proved and extended by using the stability of the localized single-valued extension property under Riesz commuting perturbations. In the last part, we give some results concerning the stability of property $(gR)$ and property $(gb)$.

DOI: 10.14232/actasm-014-785-1

AMS Subject Classification (1991): 47A10, 47A11; 47A53, 47A55

Keyword(s): localized SVEP, operators with topological uniform descent, Riesz operators, property $(gR)$ and property $(gb)$

Received April 17, 2014, and in revised form December 5, 2014. (Registered under 35/2014.)