- 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
- 1.
Bonsall FF, Duncan J: Numerical Ranges, Vol. II. Cambridge University Press, New York; 1973.
- 2.
Day MM: Uniform convexity in factor and conjugate spaces. Annals of Mathematics. Second Series 1944,45(2):375–385. 10.2307/1969275
- 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.
- 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)00408-6
- 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/S1446788700035230
- 6.
Hanner O: On the uniform convexity ofand. Arkiv för Matematik 1956, 3: 239–244. 10.1007/BF02589410
- 7.
James RC: Inner product in normed linear spaces. Bulletin of the American Mathematical Society 1947, 53: 559–566. 10.1090/S0002-9904-1947-08831-5
- 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/sm144-3-5
- 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.
- 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.2000.6727
Author information
Affiliations
Corresponding author
Rights and permissions
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:
Keywords
- Kato
- Partial Answer
- James Constant