Hereditarily normaloid operators.

Duggal, Bhagwati Prashad. "Hereditarily normaloid operators.." Extracta Mathematicae 20.2 (2005): 203-217. <http://eudml.org/doc/38787>.

@article{Duggal2005,
abstract = {A Banach space operator T belonging to B(X) is said to be hereditarily normaloid, T ∈ HN, if every part of T is normaloid; T ∈ HN is totally hereditarily normaloid, T ∈ THN, if every invertible part of T is also normaloid; and T ∈ CHN if either T ∈ THN or T - λI is in HN for every complex number λ. Class CHN is large; it contains a number of the commonly considered classes of operators. We study operators T ∈ CHN, and prove that the Riesz projection associated with a λ ∈ isoσ(T), T ∈ CHN ∩ B(H) for some Hilbert space H, is self-adjoint if and only if (T - λI)-1(0) ⊆ (T* - λI)-1(0). Operators T ∈ CHN have the important property that both T and the conjugate operator T* have the single-valued extension property at points λ which are nor in the Weyl spectrum of T; we exploit this property to prove a-Browder and a-Weyl theorems for operators T ∈ CHN.},
author = {Duggal, Bhagwati Prashad},
journal = {Extracta Mathematicae},
keywords = {Weyl's theorem; a-Weyl's theorem; a-Browder's theorem; single-valued extension property (SVEP); hereditarily normaloid operators},
language = {eng},
number = {2},
pages = {203-217},
title = {Hereditarily normaloid operators.},
url = {http://eudml.org/doc/38787},
volume = {20},
year = {2005},
}

TY - JOUR
AU - Duggal, Bhagwati Prashad
TI - Hereditarily normaloid operators.
JO - Extracta Mathematicae
PY - 2005
VL - 20
IS - 2
SP - 203
EP - 217
AB - A Banach space operator T belonging to B(X) is said to be hereditarily normaloid, T ∈ HN, if every part of T is normaloid; T ∈ HN is totally hereditarily normaloid, T ∈ THN, if every invertible part of T is also normaloid; and T ∈ CHN if either T ∈ THN or T - λI is in HN for every complex number λ. Class CHN is large; it contains a number of the commonly considered classes of operators. We study operators T ∈ CHN, and prove that the Riesz projection associated with a λ ∈ isoσ(T), T ∈ CHN ∩ B(H) for some Hilbert space H, is self-adjoint if and only if (T - λI)-1(0) ⊆ (T* - λI)-1(0). Operators T ∈ CHN have the important property that both T and the conjugate operator T* have the single-valued extension property at points λ which are nor in the Weyl spectrum of T; we exploit this property to prove a-Browder and a-Weyl theorems for operators T ∈ CHN.
LA - eng
KW - Weyl's theorem; a-Weyl's theorem; a-Browder's theorem; single-valued extension property (SVEP); hereditarily normaloid operators
UR - http://eudml.org/doc/38787
ER -