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On Weyl’s theorem. (English) Zbl 0814.47002
Summary: Let $$X$$ be a complex Banach space. If $$T\in {\mathcal B}(X)$$ is simply polar and if for each finite-dimensional eigenspace $$M$$ there is an invariant subspace of $$T$$ that is complementary to $$M$$, then Weyl’s Theorem holds for $$T$$ in the regular region.

##### MSC:
 47A10 Spectrum, resolvent 47A15 Invariant subspaces of linear operators