On S-Weyl’s theorem and property (t) for some classes of operators

In this paper we consider two new variants of the classical Weyl ’s theorem for operators defined on Banach spaces. These variants called S-Weyl’s theorem and property (t) are stronger than the more classical variants of Weyl’s theorem, as a-Weyl’s theorem and property \((\omega )\) $(\omega )$ studied by several authors. In particular, we explore these two new variants for operators that commute with an injective quasi-nilpotent operators.