Journal of Inequalities and Applications

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The James constant of normalized norms on

Journal of Inequalities and Applications20062006:026265

https://doi.org/10.1155/JIA/2006/26265

©  Nilsrakoo and Saejung 2006

Received: 28 June 2005

Accepted: 13 September 2005

Published: 4 May 2006

Abstract

We introduce a new class of normalized norms on which properly contains all absolute normalized norms. We also give a criterion for deciding whether a given norm in this class is uniformly nonsquare. Moreover, an estimate for the James constant is presented and the exact value of some certain norms is computed. This gives a partial answer to the question raised by Kato et al.

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Authors’ Affiliations

(1)
Department of Mathematics, Khon Kaen University
(2)
Department of Mathematics, Statistics and Computer, Ubon Rajathanee University

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Copyright

© Nilsrakoo and Saejung 2006

This article is published under license to BioMed Central Ltd. 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.