Weyl's theorem for commuting tuples of paranormal and $\ast $-paranormal operators

Abstract

We show that a commuting pair $T=(T_1,T_2)$ of $\ast $-paranormal operators $T_1$ and $T_2$ with quasitriangular property satisfies Weyl’s theorem-I, that is, $$ \sigma _{\rm T}(T)\setminus \sigma _{\rm T_W}(T)=\pi _{00}(T) $$ and a commuting pair of para