The James constant of normalized norms on

Weerayuth Nilsrakoo; Satit Saejung

doi:10.1155/JIA/2006/26265

Research Article
Open Access

The James constant of normalized norms on

Weerayuth Nilsrakoo^{1, 2} and
Satit Saejung¹Email author

Journal of Inequalities and Applications20062006:026265

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

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.

Keywords

Kato
Partial Answer
James Constant

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Authors’ Affiliations

(1)

Department of Mathematics, Khon Kaen University, Khon Kaen, 40002, Thailand

(2)

Department of Mathematics, Statistics and Computer, Ubon Rajathanee University, Ubon Ratchathani, 34190, Thailand

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Copyright

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.