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Compactness properties for perturbed semigroups and application to transport equation

Part of: Integral, integro-differential, and pseudodifferential operators General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Khalid Latrach
Khalid Latrach
Affiliation:
Université de CorseDépartement de Mathématiques 20250 CorteFrance
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Abstract

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Using the comparsion results for positive compact operators by Aliprantis and Burkinshow, Mokhtar Kharroubi investigated cimpactness properties of positive semigroups on Banach latttices. The aim of this paper is to study these properties in general Banach spaces (without positivity). Our results generalize a part fo those obtained by Mokhtar-Kharroubi to general Banach spaces context. More specifically, we derive conditions which ensure the compactness of the remainder term Rn(t) for some inteter n. The improvement here is that it can applied directly to the neutron transport equation for a wide class of collision operators.

MSC classification

Secondary: 47A10: Spectrum, resolvent 47A55: Perturbation theory 47G20: Integro-differential operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 1 , August 2000 , pp. 25 - 40
Copyright
Copyright © Australian Mathematical Society 2000

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