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# Essential approximate point and essential defect spectrum of a sequence of linear operators in Banach spaces

### 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.

### 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 Milestones Received 20/04/2018; Revised 03 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},
URL = {http://mfat.imath.kiev.ua/article/?id=1244},
}

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