Some spectral properties in Banach spaces and application to transport theory

Abstract

In this paper, by using the notion of the Bochner measurability, we establish some properties concerning some classes of $$C_0$$ -semigroups in Banach spaces. After, we will apply them in the framework of the transport theory in order to obtain compactness properties giving a good comprehension of the time asymptotic behavior of the solutions for the associated Cauchy problems. Moreover, by using the concept of the Hausdorff measure of noncompactness, we obtain some results incoming within the framework of the Fredholm theory. Also, a fine description of the Schechter essential spectrum of a closed densely defined operators is given.