A note on Weyl's theorem for $\ast$-paranormal operators
Commun. Korean Math. Soc. 2012 Vol. 27, No. 3, 565-570
https://doi.org/10.4134/CKMS.2012.27.3.565
Printed September 1, 2012
An Hyun Kim
Changwon National University
Abstract : 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
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