Weyl's Theorem, a‐Weyl's Theorem, and Local Spectral Theory

By R. Curto, Y. Han. 2002

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Necessary and sufficient conditions are given for a Banach space operator with the single‐valued extension property to satisfy Weyl's theorem and a‐Weyl's theorem. It is shown that if T or T* has the single‐valued extension property and T is transaloid, then Weyl's theorem holds for f(T)for every f∈H(σ(T)). When T* has the single‐valued extension property, T is transaloid and T is a‐isoloid, then a‐Weyl's theorem holds for f(T) for every f∈H(σ(T)). It is also proved that if T or T* has the single‐valued extension property, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d490fe632d911dba8c0fb149bee6bf07c3222f9b