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.

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Title

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

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},
}