• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.565-570
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• 2012

In this note we investigate Weyl's theorem for *-paranormal operators on a separable infinite dimensional Hilbert space. We prove that if T is a *-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.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.77-95
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• 2012

For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.