"Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and "generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If T or T* is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized Weyl's theorem holds for f(T), so Weyl's theorem holds for f(T), where H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T). Moreover, if T* is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized a-Weyl's theorem holds for f(T) and hence a-Weyl's theorem holds for f(T).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-5,
author = {Xiaohong Cao and Maozheng Guo and Bin Meng},
title = {Weyl type theorems for p-hyponormal and M-hyponormal operators},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {177-188},
zbl = {1075.47011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-5}
}
Xiaohong Cao; Maozheng Guo; Bin Meng. Weyl type theorems for p-hyponormal and M-hyponormal operators. Studia Mathematica, Tome 162 (2004) pp. 177-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-5/