Resumen de Hereditarily normaloid operators

B. P. Duggal

• A Banach space operator T belonging to B(X) is said to be hereditarily normaloid, T Î HN, if every part of T is normaloid; T Î HN is totally hereditarily normaloid, T Î THN, if every invertible part of T is also normaloid; and T Î CHN if either T Î THN or T - ?I is in HN for every complex number ?. Class CHN is large; it contains a number of the commonly considered classes of operators. We study operators T Î CHN, and prove that the Riesz projection associated with a ? Î isos(T), T Î CHN n B(H) for some Hilbert space H, is self-adjoint if and only if (T - ?I)-1(0) Í (T* - ?I)-1(0). Operators T Î CHN have the important property that both T and the conjugate operator T* have the single-valued extension property at points ? which are nor in the Weyl spectrum of T; we exploit this property to prove a-Browder and a-Weyl theorems for operators T Î CHN.