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Another note on Weyl’s theorem. (English) Zbl 0873.47001
Summary: “Weyl’s theorem holds” for an operator \(T\) on a Banach space \(X\) when the complement in the spectrum of the “Weyl spectrum” coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity. This is close to, but not quite the same as, equality between the Weyl spectrum and the “Browder spectrum”, which in turn ought to, but does not, guarantee the spectral mapping theorem for the Weyl spectrum of polynomials in \(T\). In this note we try to explore these distinctions.

MSC:
47A10 Spectrum, resolvent
47A60 Functional calculus for linear operators
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