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  • Research Article
  • Open Access

The James constant of normalized norms on

Journal of Inequalities and Applications20062006:026265

  • Received: 28 June 2005
  • Accepted: 13 September 2005
  • Published:


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.


  • Kato
  • Partial Answer
  • James Constant


Authors’ Affiliations

Department of Mathematics, Khon Kaen University, Khon Kaen, 40002, Thailand
Department of Mathematics, Statistics and Computer, Ubon Rajathanee University, Ubon Ratchathani, 34190, Thailand


  1. Bonsall FF, Duncan J: Numerical Ranges, Vol. II. Cambridge University Press, New York; 1973.View ArticleGoogle Scholar
  2. Day MM: Uniform convexity in factor and conjugate spaces. Annals of Mathematics. Second Series 1944,45(2):375–385. 10.2307/1969275MATHMathSciNetView ArticleGoogle Scholar
  3. Dhompongsa S, Kaewkhao A, Saejung S: Uniform smoothness and-convexity of-direct sums. Journal of Nonlinear and Convex Analysis 2005,6(2):327–338.MATHMathSciNetGoogle Scholar
  4. Dhompongsa S, Kaewkhao A, Tasena S: On a generalized James constant. Journal of Mathematical Analysis and Applications 2003,285(2):419–435. 10.1016/S0022-247X(03)00408-6MATHMathSciNetView ArticleGoogle Scholar
  5. Gao J, Lau K-S: On the geometry of spheres in normed linear spaces. Journal of Australian Mathematical Society. Series A 1990,48(1):101–112. 10.1017/S1446788700035230MATHMathSciNetView ArticleGoogle Scholar
  6. Hanner O: On the uniform convexity ofand. Arkiv för Matematik 1956, 3: 239–244. 10.1007/BF02589410MATHMathSciNetView ArticleGoogle Scholar
  7. James RC: Inner product in normed linear spaces. Bulletin of the American Mathematical Society 1947, 53: 559–566. 10.1090/S0002-9904-1947-08831-5MATHMathSciNetView ArticleGoogle Scholar
  8. Kato M, Maligranda L, Takahashi Y: On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces. Studia Mathematica 2001,144(3):275–295. 10.4064/sm144-3-5MATHMathSciNetView ArticleGoogle Scholar
  9. Mitani K-I, Saito K-S: The James constant of absolute norms on. Journal of Nonlinear and Convex Analysis 2003,4(3):399–410.MATHMathSciNetGoogle Scholar
  10. Saito K-S, Kato M, Takahashi Y: Von Neumann-Jordan constant of absolute normalized norms on. Journal of Mathematical Analysis and Applications 2000,244(2):515–532. 10.1006/jmaa.2000.6727MATHMathSciNetView ArticleGoogle Scholar


© 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.