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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Subspaces of the nonstandard hull of a normed space


Authors: C. Ward Henson and L. C. Moore
Journal: Trans. Amer. Math. Soc. 197 (1974), 131-143
MSC: Primary 46B99; Secondary 02H25
MathSciNet review: 0365098
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Abstract: Normed spaces which are isomorphic to subspaces of the nonstandard hull of a given normed space are characterized. As a consequence it is shown that a normed space is B-convex if and only if the nonstandard hull contains no subspace isomorphic to $ {l_1}$ and a Banach space is super-reflexive if and only if the nonstandard hull is reflexive. Also, embeddings of second dual spaces into the nonstandard hull are studied. In particular, it is shown that the second dual space of a normed space E is isometric to a complemented subspace of the nonstandard hull of E.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0365098-7
PII: S 0002-9947(1974)0365098-7
Article copyright: © Copyright 1974 American Mathematical Society