Ultrapowers and local properties of Banach spaces
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 by Jacques Stern PDF
 Trans. Amer. Math. Soc. 240 (1978), 231252 Request permission
Abstract:
The present paper is an approach to the local theory of Banach spaces via the ultrapower construction. It includes a detailed study of ultrapowers and their dual spaces as well as a definition of a new notion, the notion of a uextension of a Banach space. All these tools are used to give a unified definition of many classes of Banach spaces characterized by local properties (such as the ${\mathcal {L}_p}$spaces). Many examples are given; also, as an application, it is proved that any ${\mathcal {L}_p}$space, $1 < p < \infty$, has an ultrapower which is isomorphic to an ${L_p}$space.References

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Additional Information
 © Copyright 1978 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 240 (1978), 231252
 MSC: Primary 46B99; Secondary 03C20, 46E30
 DOI: https://doi.org/10.1090/S00029947197804895940
 MathSciNet review: 489594