Abstract
This paper is devoted to an investigation of the relationship between the essential approximate point spectrum (respectively, the essential defect spectrum) of a sequ\-ence of closed linear operators $(T_n)_{n\in\mathbb{N}}$ on a Banach space $X$, and the essential approximate point spectrum (respectively, the essential defect spectrum) of a linear operator $T$ on $X$, where $(T_n)_{n\in\mathbb{N}}$ converges to $T$, in the case of convergence in generalized sense as well as in the case of the convergence compactly
Key words: Essential approximate point spectrum, essential defect spectrum, convergence in the generalized sense, convergence to zero compactly.
Full Text
Article Information
| Title | Essential approximate point and essential defect spectrum of a sequence of linear operators in Banach spaces |
| Source | Methods Funct. Anal. Topology, Vol. 25 (2019), no. 4, 373-380 |
| MathSciNet |
MR4049691 |
| Milestones | Received 20/04/2018; Revised 03/09/2019 |
| Copyright | The Author(s) 2019 (CC BY-SA) |
Authors Information
Toufik Heraiz
Department of Mathematics, University of Mohammed Boudiaf of M’sila, M’sila, Algeria
Aymen Ammar
Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Soukra Road Km 3.5, B. P. 1171, 3000, Sfax
Aref Jeribi
Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Soukra Road Km 3.5, B. P. 1171, 3000, Sfax
Citation Example
Toufik Heraiz, Aymen Ammar, and Aref Jeribi, Essential approximate point and essential defect spectrum of a sequence of linear operators in Banach spaces, Methods Funct. Anal. Topology 25
(2019), no. 4, 373-380.
BibTex
@article {MFAT1244,
AUTHOR = {Toufik Heraiz and Aymen Ammar and Aref Jeribi},
TITLE = {Essential approximate point and essential defect spectrum of a sequence of linear operators in Banach spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {4},
PAGES = {373-380},
ISSN = {1029-3531},
MRNUMBER = {MR4049691},
URL = {http://mfat.imath.kiev.ua/article/?id=1244},
}
