$S$-Weyl's theorem for bounded linear operators on Banach spaces

Abstract

In this paper we consider a new variant of the classical Weyl type theorems for operators defined on Banach spaces. This variant, called {\em $S$-Weyl's theorem} entails two other variants, $a$-Weyl's theorem and property $(w)$, studied by different authors in the last two decades. The theory is also exemplified by considering many classes of operators that satisfy it. In particular, the theory is exemplified for Toeplitz operators defined on the Hardy space $H^2 (\mathbf T)$, where $\mathbf T$ is the unit circle.