Compactness properties for perturbed semigroups and application to transport equation

Khalid Latrach
2000 Journal of the Australian Mathematical Society  
Using the comparison results for positive compact operators by Aliprantis and Burkinshow, Mokhtar-Kharroubi investigated compactness properties of positive semigroups on Banach lattices. The aim of this paper is to study these properties in general Banach spaces (without positivity). Our results generalize a part of those obtained by Mokhtar-Kharroubi to general Banach spaces context. More specifically, we derive conditions which ensure the compactness of the remainder term R n (t) for some
more » ... n (t) for some integer n. The improvement here is that it can applied directly to the neutron transport equation for a wide class of collision operators. 2000 Mathematics subject classification: primary 47A10,47A55, 47G20. [6, 10]) that if K e J£?(X), then T + K generates a strongly continuous semigroup {V(t), t > 0} given by the Dyson-Phillips expansion where U 0 (t) = U(t), Uj(t) = [ U(s)KUj^(t -s)ds (j > 1).
doi:10.1017/s1446788700001828 fatcat:exrcwfcluffgpk7i47dbn3urom