Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Perturbation Results on Semi-Fredholm Operators and Applications | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 284526 13 pages doi 2009 284526 Research Article Perturbation Results on Semi-Fredholm Operators and Applications Boulbeba Abdelmoumen and Hamadi Baklouti Departement de Maths Faculte des Sciences de Sfax B. P. 1171 3000 Sfax Tunisia Correspondence should be addressed to Boulbeba Abdelmoumen Received 14 July 2009 Accepted 26 September 2009 Recommended by Jozef Banas We give some results concerning stability in the Fredholm operators and Browder operators set via the concept of measure of noncompactness. Moreover we prove some localization results on the essential spectra of bounded operators on Banach space. As application we describe the essential spectra of weighted shift operators. Finally we describe the spectra of polynomially compact operators and we use the obtained results to study the solvability for operator equations in Banach spaces. Copyright 2009 B. Abdelmoumen and H. Baklouti. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Throughout this paper X denotes an infinite dimensional complex Banach space. We denote by L X the space of all bounded linear operators on X. The subspace of all compact operators of L X is denoted by K X . We write N T c X for the null space and R T c X for the range of T. The nullity n T of T is defined as the dimension of N T and the deficiency d T of T is defined as the codimension of R T in X. The set of upper lower semi-Fredholm operators are defined respectively by X T e L X n T TO and R T is closed in X and respectively O- X T e L X d T to . We use X X n O- X for the set of Fredholm operators in L X and Ọ X X u - X for the set of semi-Fredholm operators in L X . If T e Ọ X then i T n T - d T is called the index
