On Completely Continuous Integration Operators of a Vector Measure

Autores UPV
Año
Revista JOURNAL OF CONVEX ANALYSIS

Abstract

Let m be a vector measure taking values in a Banach space X. We prove that if the integration operator Im : L1(m) -> X, is completely continuous and X is Asplund, then m has finite variation and L1(|m|) = L1(m).