A Note on Property (gb) and Perturbations

Qingping Zeng and Huaijie Zhong

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: An operator T ∈ ℬ(X) defined on a Banach space X satisfies property (gb) if the complement in the approximate point spectrum σa(T) of the upper semi‐B‐Weyl spectrum σSBF+-(T) coincides with the set Π(T) of all poles of the resolvent of T. In this paper, we continue to study property (gb) and the stability of it, for a bounded linear operator T acting on a Banach space, under perturbations by nilpotent operators, by finite rank operators, and by quasinilpotent operators commuting with T. Two counterexamples show that property (gb) in general is not preserved under commuting quasi‐nilpotent perturbations or commuting finite rank perturbations.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2012/523986

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:523986

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().