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31 January 2005 On the modulus of $U$-convexity
Satit Saejung
Abstr. Appl. Anal. 2005(1): 59-66 (31 January 2005). DOI: 10.1155/AAA.2005.59


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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Satit Saejung. "On the modulus of $U$-convexity." Abstr. Appl. Anal. 2005 (1) 59 - 66, 31 January 2005.


Published: 31 January 2005
First available in Project Euclid: 19 April 2005

zbMATH: 1099.46015
MathSciNet: MR2142156
Digital Object Identifier: 10.1155/AAA.2005.59

Rights: Copyright © 2005 Hindawi

Vol.2005 • No. 1 • 31 January 2005
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