WEYL TYPE THEOREMS FOR ALGEBRIACALLY CLASS $p$-$wA(s,t)$ OPERATORS

In this paper, we study Weyl type theorems for $f(T)$ , where $T$ is algebraically class $p$ - $wA(s, t)$ operator with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$ and $f$ is an analytic function defined on an open neighborhood of the spectrum of $T$ . Also we show that if $A , B^{*} \in B(\mathcal{H}) $ are class $p$ - $wA(s, t)$ operators with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$ , then generalized Weyl's theorem , a- Weyl's theorem, property $(w)$ , property $(gw)$ and generalized a- Weyl's theorem holds for $f(d_{AB})$ for every $f \in H(\sigma(d_{AB})$ , where $ d_{AB}$ denote the generalized derivation $\delta_{AB}:B(\mathcal{H})\rightarrow B(\mathcal{H})$ defined by $\delta_{AB}(X)=AX-XB$ or the elementary operator $\Delta_{AB}:B(\mathcal{H})\rightarrow B(\mathcal{H})$ defined by $\Delta_{AB}(X)=AXB-X$ .