- Research Article
- Open access
- Published:
The James constant of normalized norms on
Journal of Inequalities and Applications volume 2006, Article number: 026265 (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.
References
Bonsall FF, Duncan J: Numerical Ranges, Vol. II. Cambridge University Press, New York; 1973.
Day MM: Uniform convexity in factor and conjugate spaces. Annals of Mathematics. Second Series 1944,45(2):375–385. 10.2307/1969275
Dhompongsa S, Kaewkhao A, Saejung S: Uniform smoothness and-convexity of-direct sums. Journal of Nonlinear and Convex Analysis 2005,6(2):327–338.
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)00408-6
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/S1446788700035230
Hanner O: On the uniform convexity ofand. Arkiv för Matematik 1956, 3: 239–244. 10.1007/BF02589410
James RC: Inner product in normed linear spaces. Bulletin of the American Mathematical Society 1947, 53: 559–566. 10.1090/S0002-9904-1947-08831-5
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/sm144-3-5
Mitani K-I, Saito K-S: The James constant of absolute norms on. Journal of Nonlinear and Convex Analysis 2003,4(3):399–410.
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.2000.6727
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Nilsrakoo, W., Saejung, S. The James constant of normalized norms on. J Inequal Appl 2006, 026265 (2006). https://doi.org/10.1155/JIA/2006/26265
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/JIA/2006/26265