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 Some New Properties in Fredholm Theory, Schechter Essential Spectrum, and Application to Transport Theory | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 852676 14 pages doi 2008 852676 Research Article Some New Properties in Fredholm Theory Schechter Essential Spectrum and Application to Transport Theory Boulbeba Abdelmoumen 1 Abdelkader Dehici 2 Aref Jeribi 1 and Maher Mnif1 1 Department of Mathematics Faculty of Science ofSfax Sfax 3018 Tunisia 2 Departement des Sciences Exactes Universite 8 Mai 1945 BP 401 Guelma 24000 Algeria Correspondence should be addressed to Aref Jeribi Received 19 April 2007 Revised 11 July 2007 Accepted 24 September 2007 Recommended by Nikolaos S. Papageorgiou The theory of measures of noncompactness has many applications on topology functional analysis and operator theory. In this paper we consider one axiomatic approach to this notion which includes the most important classical definitions. We give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover we establish a fine description of the Schechter essential spectrum of closed densely defined operators. These results are exploited to investigate the Schechter essential spectrum of a multidimensional neutron transport operator. Copyright 2008 Boulbeba Abdelmoumen et al. 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 Let X ll ll be an infinite-dimensional Banach space. The open ball of X will be denoted by BX and its closure by BX. We denote by C X resp. L X the set of all closed densely defined linear operators resp. the space of all bounded linear operators on X. The set of all compact operators of L X is designed by K X . Let T G C X we write N T c X for the null space and R T c X for the range of T. We set a T dim N T and f T codim R T . The set of .
