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 first show a representation theorem of measures of noncompactness defined 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 fixed point theorem for norm-to-weak continuous mappings.

Mathematics Subject Classification (2010):

• Primary: 47H09
• 46B50
• 47H20
• 47H10

Key words:

• Measure of noncompactness
• Banach space
• global attractor of operator semigroup
• fixed point
• Banach space