Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (6): 1285-1304.doi: 10.1016/S0252-9602(15)30054-0

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ON A CHARACTERIZATION OF THE S-ESSENTIAL SPECTRA OF THE SUM AND THE PRODUCT OF TWO OPERATORS AND APPLICATION TO A TRANSPORT OPERATOR

Salma CHARFI, Sassia RAHALI   

  1. Département de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, Route de soukra Km 3.5, B. P 1171, 3000, Sfax, Tunisie
  • Received:2014-11-30 Revised:2014-08-19 Online:2015-11-01 Published:2015-11-01

Abstract:

In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L1([-a, a] × [-1, 1]) (a > 0).

Key words: Fredholm operator, Fredholm perturbation, S-essential spectra, transport operator

CLC Number: 

  • 47A13
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