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On the modulus of U‐convexity

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  • Satit Saejung

Abstract

We prove that the moduli of U‐convexity, introduced by Gao (1995), of the ultrapower X˜ of a Banach space X and of X itself coincide whenever X is super‐reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove that uX(1) > 0 implies that both X and the dual space X∗ of X have uniform normal structure and hence the “worth” property in Corollary 7 of Mazcuñán‐Navarro (2003) can be discarded.

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Handle: RePEc:wly:jnlaaa:v:2005:y:2005:i:1:p:59-66
DOI: 10.1155/AAA.2005.59
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