Some characterizations of the analytic Radon-Nikodým property in Banach spaces
A Banach space X for which every bounded X-valued analytic function on the open unit disk has radial limits almost everywhere is said to have the analytic Radon-Nikodym property (aRNP). It is shown that X has aRNP if every operator from \(L^ 1\) to X which factors through \(L^ 1/H^ 1_ 0\) is representable, a characterization which is similar to that of RNP. Some immediate applications to properties of subspaces of \(L^ 1/H^ 1_ 0\) are indicated. The characterization also gives rise to a reasonable definition of aRNP for real spaces.
scientific article; zbMATH DE number 4086291
scientific article