## Abstract and Applied Analysis

### On the modulus of $U$-convexity

Satit Saejung

#### Abstract

We prove that the moduli of $U$-convexity, introduced by Gao (1995), of the ultrapower $\widetilde{X}$ 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.

#### Article information

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

Dates
First available in Project Euclid: 19 April 2005

https://projecteuclid.org/euclid.aaa/1113922223

Digital Object Identifier
doi:10.1155/AAA.2005.59

Mathematical Reviews number (MathSciNet)
MR2142156

Zentralblatt MATH identifier
1099.46015

#### Citation

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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