### 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},
}