Abstract and Applied Analysis

On the modulus of $U$-convexity

Satit Saejung

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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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Abstr. Appl. Anal., Volume 2005, Number 1 (2005), 59-66.

First available in Project Euclid: 19 April 2005

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Saejung, Satit. On the modulus of $U$-convexity. Abstr. Appl. Anal. 2005 (2005), no. 1, 59--66. doi:10.1155/AAA.2005.59. https://projecteuclid.org/euclid.aaa/1113922223

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