## Articulo

• Similares en SciELO

## versión impresa ISSN 0716-0917

### Proyecciones (Antofagasta) vol.38 no.3 Antofagasta ago. 2019

#### http://dx.doi.org/10.22199/issn.0717-6279-2019-03-0026

Articles

Upper triangular operator matrices and limit points of the essential spectrum

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

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

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

Abstract

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

Acknowledgement

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