数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (2): 546-556.doi: 10.1016/S0252-9602(14)60027-8

• 论文 • 上一篇    下一篇

RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

Bilel KRICHEN   

  1. Department of Mathematics, Preparatory Engineering Institute, Road Menzel Chaker Km 0.5, BP 1172-3018, Sfax Tunisia.
  • 收稿日期:2013-02-25 修回日期:2013-10-09 出版日期:2014-03-20 发布日期:2014-03-20

RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

Bilel KRICHEN   

  1. Department of Mathematics, Preparatory Engineering Institute, Road Menzel Chaker Km 0.5, BP 1172-3018, Sfax Tunisia.
  • Received:2013-02-25 Revised:2013-10-09 Online:2014-03-20 Published:2014-03-20

摘要:

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation
results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter´s and approximate essential spectrum.

关键词: Demicompact linear operator, relative essential spectrum, Fredholm and semi-Fredholm operators, measure of noncompactness

Abstract:

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation
results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter´s and approximate essential spectrum.

Key words: Demicompact linear operator, relative essential spectrum, Fredholm and semi-Fredholm operators, measure of noncompactness

中图分类号: 

  • 47A10