Hereditarily polaroid operators, SVEP and Weyl's theorem |
| |
Authors: | B.P. Duggal |
| |
Affiliation: | 8 Redwood Grove, Northfield Avenue, Ealing, London W5 4SZ, United Kingdom |
| |
Abstract: | A Banach space operator T∈B(X) is hereditarily polaroid, T∈HP, if every part of T is polaroid. HP operators have SVEP. It is proved that if T∈B(X) has SVEP and R∈B(X) is a Riesz operator which commutes with T, then T+R satisfies generalized a-Browder's theorem. If, in particular, R is a quasi-nilpotent operator Q, then both T+Q and T∗+Q∗ satisfy generalized a-Browder's theorem; furthermore, if Q is injective, then also T+Q satisfies Weyl's theorem. If A∈B(X) is an algebraic operator which commutes with the polynomially HP operator T, then T+N is polaroid and has SVEP, f(T+N) satisfies generalized Weyl's theorem for every function f which is analytic on a neighbourhood of σ(T+N), and f∗(T+N) satisfies generalized a-Weyl's theorem for every function f which is analytic on, and constant on no component of, a neighbourhood of σ(T+N). |
| |
Keywords: | Banach space Hereditarily polaroid operator Single valued extension property Generalized Weyl' theorem |
本文献已被 ScienceDirect 等数据库收录! |
|