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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta Aug. 2019 


Upper triangular operator matrices and limit points of the essential spectrum

M. Karmouni1 

A. Tajmouati2 

A. El Bakkali3 

1Cadi Ayyad University, Multidisciplinary Faculty, Sidi Bouzid, B.P. 4162, 46000 Safí, Morocco. e-mail :

2Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar Al Mahraz, Laboratory of Mathematical Analysis and Applications, Fez, Morocco. e-mail:

3Chouaib Doukkali University, Faculty of Science, Department of Mathematics, 24000, Eljadida, Morocco. email :


In this paper, we investigate the limit points set of essential spectrum of upper triangular operator matrices

We prove that accσe(MC) ∪ W = accσe(A) ∪ accσe(B) where W is the union of certain holes in accσe(MC), which happen to be subsets of accσe(B) ∩ accσe(A). Also, several sufficient conditions for accσe(MC) = accσe(A) ∪ accσe(B) holds are given.

Keywords : Fredholm operator; Essential spectra; Limit point; Operator matrices.

Mathematics Subject Classification (2000):  47A10; 47A11

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The authors thank the referees for his suggestions and comments thorough reading of the manuscript.


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Received: November 2017; Accepted: May 2019

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