In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f ∈ H(σ(T)). We also provide several conditions that force an operator with the SVEP to obey a-Weyl's theorem.
The author would like to precise that this paper constitute a part of his thesis [16].
@article{urn:eudml:doc:41849,
title = {a-Weyl's theorem and the single valued extension property.},
journal = {Extracta Mathematicae},
volume = {21},
year = {2006},
pages = {41-50},
zbl = {1112.47009},
mrnumber = {MR2258340},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41849}
}
Oudghiri, Mourad. a-Weyl's theorem and the single valued extension property.. Extracta Mathematicae, Tome 21 (2006) pp. 41-50. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41849/