TY - JOUR AU - Abdelmoumen, Boulbeba AU - Dehici, Abdelkader AU - Jeribi, Aref AU - Mnif, Maher PY - 2007 DA - 2007/12/02 TI - Some New Properties in Fredholm Theory, Schechter Essential Spectrum, and Application to Transport Theory JO - Journal of Inequalities and Applications SP - 852676 VL - 2008 IS - 1 AB - 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 a closed densely defined operators. These results are exploited to investigate the Schechter essential spectrum of a multidimensional neutron transport operator. SN - 1029-242X UR - https://doi.org/10.1155/2008/852676 DO - 10.1155/2008/852676 ID - Abdelmoumen2007 ER -