Communications of the
Korean Mathematical Society CKMS

In this paper we find some classes of operators for which Weyl's theorem holds. The main result is as follows. If $T\in\Cal{L(H)}$ satisfies the following: \roster \item"(i)" Either $T$ or $T^*$ is reduced by each of its eigenspaces; \item"(ii)" Weyl's theorem holds for $T$; \item"(iii)" $T$ is isoloid, \endroster then for every polynomial $p$, Weyl's theorem holds for $p(T)$.

Keywords: Weyl spectrum, Weyl's theorem, isoloid operators, reguloid operators

MSC numbers: 47A10, 47A53