On the modulus of U -convexity

Satit Saejung

Abstract and Applied Analysis, 2005, vol. 2005, 1-8

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 u X ( 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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:716725

DOI: 10.1155/AAA.2005.59

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