Hereditarily normaloid operators.

Duggal, Bhagwati Prashad

Extracta Mathematicae, Tome 20 (2005), p. 203-217 / Harvested from Biblioteca Digital de Matemáticas

Résumé

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.

Détail

Publié le : 2005-01-01

MR MR2195202 | Zbl 1097.47005

DMLE-ID : 1572