A Cone Characterization of Reflexive Banach Spaces Original Research Article

Let (Z, ‖ ‖) be a Banach space. Then (Z, ‖ ‖) is reflexive if and only if for each convex cone Λ admitting a bounded base in (Z*, ‖ ‖*), Λ∗ is solid in (Z, ‖ ‖). Here Z* denotes the dual of (Z, ‖ ‖) and Λ∗ denotes the polar of Λ taken in Z.