Weyl's theorem, a-Weyl's theorem, and local spectral theory

Details Weyl's theorem, a-Weyl's theorem, and local spectral theory Weyl's theorem, a-Weyl's theorem, and local spectral theory

2002-07-06

arxiv.org/abs/math/0207064v1

J. London Math. Soc. (2) 67(2003), 499-509

Mathematics

Functional Analysis

23 pages

Scientific paper

We give necessary and sufficient conditions for a Banach space operator with the single valued extension property (SVEP) to satisfy Weyl's theorem and $a$-Weyl's theorem. We show that if $T$ or $T^{\ast}$ has SVEP and $T$ is transaloid, then Weyl's theorem holds for $f(T)$ for every $f\in H(\sigma (T))$. When $T^{\ast}$ has SVEP, $T$ is transaloid and $T$ is $a$-isoloid, then $a$-Weyl's theorem holds for $f(T)$ for every $f\in H(\sigma (T))$. We also prove that if $T$ or $T^{\ast}$ has SVEP, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

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