Weyl type theorems for p-hyponormal and M-hyponormal operators

Xiaohong Cao, Maozheng Guo, and Bin Meng. "Weyl type theorems for p-hyponormal and M-hyponormal operators." Studia Mathematica 163.2 (2004): 177-188. <http://eudml.org/doc/285339>.

@article{XiaohongCao2004,
abstract = {"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).},
author = {Xiaohong Cao, Maozheng Guo, Bin Meng},
journal = {Studia Mathematica},
keywords = {Weyl's theorem; generalized Weyl's theorem; a-Weyl's theorem; generalized a-Weyl's theorem; -hyponormal operator; -hyponormal operator},
language = {eng},
number = {2},
pages = {177-188},
title = {Weyl type theorems for p-hyponormal and M-hyponormal operators},
url = {http://eudml.org/doc/285339},
volume = {163},
year = {2004},
}

TY - JOUR
AU - Xiaohong Cao
AU - Maozheng Guo
AU - Bin Meng
TI - Weyl type theorems for p-hyponormal and M-hyponormal operators
JO - Studia Mathematica
PY - 2004
VL - 163
IS - 2
SP - 177
EP - 188
AB - "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).
LA - eng
KW - Weyl's theorem; generalized Weyl's theorem; a-Weyl's theorem; generalized a-Weyl's theorem; -hyponormal operator; -hyponormal operator
UR - http://eudml.org/doc/285339
ER -