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

2002/07/06 by Raul E. Curto, Young Min Han
Mathematics · #math.FA #math.SP #msc:47A10 #msc:47A53 #msc:47A11

paper · pdf

published as J. London Math. Soc. (2) 67(2003), 499-509 · 23 pages

arxiv created 2002/07/06 · arxiv updated 2009/11/30

Abstract

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^∗ has SVEP and T is transaloid, then Weyl's theorem holds for f(T) for every f∈ H(σ(T)). When T^∗ has SVEP, T is transaloid and T is a-isoloid, then a-Weyl's theorem holds for f(T) for every f∈ H(σ(T)). We also prove that if T or T^∗ has SVEP, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

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