Weyl's theorem, a-Weyl's theorem, and local spectral theory
| dc.creator | Curto, Raul E. | |
| dc.creator | Han, Young Min | |
| dc.date | 2002-07-06 | |
| dc.date.accessioned | 2026-07-07T04:49:34Z | |
| dc.date.available | 2026-07-07T04:49:34Z | |
| dc.description | 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 $f\in H(σ(T))$. When $T^{\ast}$ has SVEP, $T$ is transaloid and $T$ is $a$-isoloid, then $a$-Weyl's theorem holds for $f(T)$ for every $f\in H(σ(T))$. 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. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0207064 | |
| dc.identifier | http://arxiv.org/abs/math/0207064 | |
| dc.identifier | J. London Math. Soc. (2) 67(2003), 499-509 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64471 | |
| dc.subject | Functional Analysis | |
| dc.subject | Spectral Theory | |
| dc.subject | 47A10; 47A53; 47A11 | |
| dc.title | Weyl's theorem, a-Weyl's theorem, and local spectral theory | |
| dc.type | text |