# Hereditarily normaloid operators.

Extracta Mathematicae (2005)

- Volume: 20, Issue: 2, page 203-217
- ISSN: 0213-8743

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topDuggal, 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 -

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