A Note on Property (gb) and Perturbations
Joint Authors
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-08-21
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Zeng, Qingping& Zhong, Huaijie. 2012. A Note on Property (gb) and Perturbations. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-10.
https://search.emarefa.net/detail/BIM-478484
Modern Language Association (MLA)
Zeng, Qingping& Zhong, Huaijie. A Note on Property (gb) and Perturbations. Abstract and Applied Analysis No. 2012 (2012), pp.1-10.
https://search.emarefa.net/detail/BIM-478484
American Medical Association (AMA)
Zeng, Qingping& Zhong, Huaijie. A Note on Property (gb) and Perturbations. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-10.
https://search.emarefa.net/detail/BIM-478484
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-478484