Journal article
WEYL'S THEOREM, $a$-WEYL'S THEOREM, AND LOCAL SPECTRAL THEORY
Journal of the London Mathematical Society, Vol.67(2), pp.499-509
04/2003
DOI: 10.1112/S0024610702004027
Abstract
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 $T^{\ast}$ has the single-valued extension property and $T$ is transaloid, then Weyl's theorem holds for $f(T)$ for every $f\in H(\sigma (T))$. When $T^{\ast}$ 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 $f\in H(\sigma(T))$. It is also proved that if $T$ or $T^{\ast}$ has the single-valued extension property, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.
Details
- Title: Subtitle
- WEYL'S THEOREM, $a$-WEYL'S THEOREM, AND LOCAL SPECTRAL THEORY
- Creators
- RAÚL E CURTO - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USAccurto@math.uiowa.eduYOUNG MIN HAN - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USAyhan@math.uiowa.edu
- Resource Type
- Journal article
- Publication Details
- Journal of the London Mathematical Society, Vol.67(2), pp.499-509
- Publisher
- Cambridge University Press; Cambridge, UK
- DOI
- 10.1112/S0024610702004027
- ISSN
- 0024-6107
- eISSN
- 1469-7750
- Number of pages
- 11
- Language
- English
- Date published
- 04/2003
- Academic Unit
- Mathematics
- Record Identifier
- 9983985857902771
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