## Subspaces of the nonstandard hull of a normed space

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- by C. Ward Henson and L. C. Moore PDF
- Trans. Amer. Math. Soc.
**197**(1974), 131-143 Request permission

## 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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## Additional Information

- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**197**(1974), 131-143 - MSC: Primary 46B99; Secondary 02H25
- DOI: https://doi.org/10.1090/S0002-9947-1974-0365098-7
- MathSciNet review: 0365098