Abstract

In this paper we study the property $(gaz)$ for a bounded linear operator $T\in L(X)$ on a Banach space $X$, introduced by Zariouh in [\emph{Property $(gz)$ for bounded linear operators}, Mat.\ Vesnik, {\bf 65(1)}(2013), 94--103], through the methods of local spectral theory. This property is a stronger variant of generalized $a$-Browder's theorem. In particular, we shall give several characterizations of property $(gaz)$, by using the localized SVEP.

Keywords: Property $(gaz)$; localized SVEP; Browder type theorems.

MSC: 47A10, 47A11, 47A53, 47A55

Pages:  314$-$326     

Volume  72 ,  Issue  4 ,  2020