Reflexivity, the dual Radon-Nikodym property, and continuity of adjoint semigroups II

AbstractIn this paper we continue the investigation on the relation between the behaviour of the adjoint of a C0-semigroup and the structure of the underlying Banach space. The following results are proved: if X lacks the RNP then X⊙*/X is nonseparable, and if X* lacks the RNP then either X*/X⊙ or X⊙⊙/X is nonseparable. The results are applied to obtain a trichotomy theorem for adjoint semigroups. Also some applications to C0-groups are given