The completion of a B-convex normed Riesz space is reflexive

AbstractIf is a B-convex normed Riesz space, then the topological completion of is a closed subspace of ∗∗, the second Banach dual of . If N=∗∗ or N=∗∗x, then N is a B-convex σ-Dedekind complete normed Riesz space which is the Banach dual of a normed Riesz space. In such a N, if u1 ⩾ u2 ⩾ … ⩾ 0 and infn{un} = 0, then limn∥un∥ = 0. This is the key step in verifying that Ogasawara's criteria that a normed Riesz space be reflexive are satisfied by ∗∗. Thus the topological completion of as a closed subspace of ∗∗ is also reflexive