Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (5): 2050-2064.doi: 10.1016/S0252-9602(12)60159-3

• Articles • Previous Articles    

ON GRAPH MEASURES IN BANACH SPACES AND DESCRIPTION OF ESSENTIAL SPECTRA OF MULTIDIMENSIONAL TRANSPORT EQUATION

Boulbeba Abdelmoumen| Aref Jeribi|Maher Mnif   

  1. Département de Mathématiques, Université|de Sfax, Faculté|des Sciences de Sfax, Route de Soukra, Km 3.5, B. P. 1171, 3000, Sfax, Tunisie
  • Received:2010-01-08 Revised:2012-01-14 Online:2012-09-20 Published:2012-09-20

Abstract:

In this paper, we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness. Moreover, we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on
the behavior of essential spectra of such closed densely defined linear operators on Banach spaces. These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.

Key words: measures of noncompactness and weak noncompactness in Banach spaces, Fredholm operators, essential spectra

CLC Number: 

  • 47A10
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