Compactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operators

Abstract

Using compactness properties of bounded subsets of spaces of vector measure integrable functions and a representation theorem for q-convex Banach lattices, we prove a domination theorem for operators between Banach lattices. We generalize in this way several classical factorization results for operators between these spaces, as psumming operators.

Keywords

• Compactness
• Vector measures
• Integration
• Factorization