Hereditarily polaroid operators, SVEP and Weyl's theorem

23Citations
Citations of this article
2Readers
Mendeley users who have this article in their library.
Get full text

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). © 2007 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Duggal, B. P. (2008). Hereditarily polaroid operators, SVEP and Weyl’s theorem. Journal of Mathematical Analysis and Applications, 340(1), 366–373. https://doi.org/10.1016/j.jmaa.2007.08.047

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free