Equivalence properties for the Radon-Nikodym property types and the complete continuity property types of Banach Spaces
AbstractWe show that the types I- and II-Λ-Radon-Nikodym Property of Banach spaces on the one hand, and the I- and II-Λ-Complete Continuity Property on the other, are equivalent properties whenever Λ is an ordering subset of a discrete abelian group.
Mathematics Subject Classification (2000): Primary 46E40, 46G10; Secondary 43A46, 43A17.
Key words: Radon-Nikodym Property, Complete Continuity Property, vector measures, discrete abelian group.
Quaestiones Mathematicae 26(2003), 419–426