NEW RESULTS OF ESSENTIAL APPROXIMATE AND DEFECT POINT SPECTRUM BY USING THE GAP CONVERGENCE

Aymen Ammar, Toufik Heraiz, Aref Jeribi

DOI Number
https://doi.org/10.22190/FUMI180409036A
First page
529
Last page
539

Abstract


This paper focuses on exploring the relationship between the essential approximate point spectrum (and the essential defect spectrum) of a sequence of closed
linear operators (Tn)n2N acting on a Banach space X, and the corresponding spectra
of a linear operator T on X. We examine this relationship under both generalized
convergence and compact convergence conditions for the sequence (Tn)n2N converging
to T.

Keywords

essential approximate point spectrum, essential defect spectrum, convergence by the gap, convergence compactly.

Keywords


Essential approximate point spectrum, essential defect spectrum, Convergence to zero compactly, Convergence in the generalized sense.

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References


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DOI: https://doi.org/10.22190/FUMI180409036A

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