Electronic Journal of Differential Equations, Vol. 2007(2007), No. 11, pp. 1-16. Title: On the essential spectra of matrix operators and applications Authors: Mondher Damak (Univ. de Sfax, Tunisie) Aref Jeribi (Univ. de Sfax, Tunisie) Abstract: In this paper, we investigate the essential spectra of some matrix operators on Banach spaces. The results obtained are used for describing the essential spectra of differential operators. Submitted October 3, 2006. Published January 8, 2007. Math Subject Classifications: 34L40, 47A11, 47A53, 47B50. Key Words: Matrix operators; essential spectra; Fredholm perturbation.