On measure of noncompactness and application to global attractors of operator semigroups

Abstract

Based on the recent development of the theory of measures of noncompactness, we rst show a representation theorem of measures of noncompactness dened on Banach spaces. Then, in terms of measure of noncompactness, we present some new characterizations of the existence of global attractors for norm-to-weak continuous semigroups, and a xed point theorem for norm-to-weak continuous mappings.

Key words: Measure of noncompactness, Banach space, global attractor of operator semi-group, fixed point, Banach space.