Title: The completion of a B-convex normed Riesz space is reflexive
Abstract: If 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.
Publication Year: 1973
Publication Date: 1973-02-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 6
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