Communications of the
Korean Mathematical Society CKMS

In this note we investigate Weyl's theorem for $\ast$-paranormal operators on a separable infinite dimensional Hilbert space. We prove that if $T$ is a $\ast$-paranormal operator satisfying Property (E) - $(T-\lambda I) H_T(\{\lambda\})$ is closed for each $\lambda\in\mathbb{C}$, where $H_T(\{\lambda\})$ is a local spectral subspace of $T$, then Weyl's theorem holds for $T$.

Keywords: Weyl's theorem, $\ast$-paranormal operators, Property (E)

MSC numbers: Primary 47A10, 47A11, 47A53