Some inequalities concerning the weakly convergent sequence coefficient in Banach spaces. (English) Zbl 1151.26324

Summary: We establish two inequalities concerning the weakly convergent sequence coefficient and other parameters, which enable us to obtain some sufficient conditions for normal structure.


26D15 Inequalities for sums, series and integrals
46B20 Geometry and structure of normed linear spaces
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[1] W. L. Bynum, “Normal structure coefficients for Banach spaces,” Pacific Journal of Mathematics, vol. 86, no. 2, pp. 427-436, 1980. · Zbl 0442.46018
[2] B. Sims and M. A. Smyth, “On some Banach space properties sufficient for weak normal structure and their permanence properties,” Transactions of the American Mathematical Society, vol. 351, no. 2, pp. 497-513, 1999. · Zbl 0909.47041
[3] S. Dhompongsa, P. Piraisangjun, and S. Saejung, “Generalised Jordan-von Neumann constants and uniform normal structure,” Bulletin of the Australian Mathematical Society, vol. 67, no. 2, pp. 225-240, 2003. · Zbl 1034.46018
[4] S. Dhompongsa, A. Kaewkhao, and S. Tasena, “On a generalized James constant,” Journal of Mathematical Analysis and Applications, vol. 285, no. 2, pp. 419-435, 2003. · Zbl 1030.46010
[5] A. Jiménez-Melado, E. Llorens-Fuster, and S. Saejung, “The von Neumann-Jordan constant, weak orthogonality and normal structure in Banach spaces,” Proceedings of the American Mathematical Society, vol. 134, no. 2, pp. 355-364, 2006. · Zbl 1102.46009
[6] M. Kato, L. Maligranda, and Y. Takahashi, “On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces,” Studia Mathematica, vol. 144, no. 3, pp. 275-295, 2001. · Zbl 0997.46009
[7] S. Saejung, “On James and von Neumann-Jordan constants and sufficient conditions for the fixed point property,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1018-1024, 2006. · Zbl 1107.47041
[8] F. Wang and C. Yang, “Some sufficient conditions for uniform normal structure in Banach spaces,” Acta Mathematica Sinica, vol. 51, no. 4, pp. 761-768, 2008. · Zbl 1174.46006
[9] A. Jiménez-Melado and E. Llorens-Fuster, “The fixed point property for some uniformly nonsquare Banach spaces,” Bollettino della Unione Matemàtica Italiana. Serie A, vol. 10, no. 3, pp. 587-595, 1996. · Zbl 0874.46010
[10] E. Casini, “About some parameters of normed linear spaces,” Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Fisiche. Serie VIII, vol. 80, no. 1-2, pp. 11-15, 1986. · Zbl 0637.46019
[11] J. Gao and K.-S. Lau, “On the geometry of spheres in normed linear spaces,” Journal of Australian Mathematical Society. Series A, vol. 48, no. 1, pp. 101-112, 1990. · Zbl 0687.46012
[12] J. A. Clarkson, “The von Neumann-Jordan constant for the Lebesgue spaces,” Annals of Mathematics, vol. 38, no. 1, pp. 114-115, 1937. · Zbl 0016.03002
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