This is an announcement for the paper “The dual Radon - Nikodym property for finitely generated Banach $C(K)$-Modules” by Arkady Kitoverhttps://arxiv.org/find/math/1/au:+Kitover_A/0/1/0/all/0/1, Mehmet Orhonhttps://arxiv.org/find/math/1/au:+Orhon_M/0/1/0/all/0/1.
Abstract: We extend the well-known criterion of Lotz for the dual Radon-Nikodym property (RNP) of Banach lattices to finitely generated Banach $C(K)$-modules and Banach $C(K)$-modules of finite multiplicity. Namely, we prove that if $X$ is a Banach space from one of these classes then its Banach dual $X^*$ has the RNP iff $X$ does not contain a closed subspace isomorphic to $\ell_1$.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1707.04655