Some characterizations of the analytic Radon-Nikodým property in Banach spaces

The analytic Radon-Nikodým property for a complex Banach space X is characterized in several ways analogous to the common characterizations of the Radon-Nikodým property. For example, the Banach space X has the analytic Radon-Nikodým property if and only if any operator from L¹ to X that factors through L¹/H₀¹ is representable. The characterizations are used to study complemented subspaces of L¹/H₀¹ and to define the analytic Radon-Nikodým property for real Banach spaces.