Abstract and Applied Analysis
Volume 2005 (2005), Issue 1, Pages 59-66
doi:10.1155/AAA.2005.59
On the modulus of U-convexity
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Received 12 January 2004
Copyright © 2005 Satit Saejung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.