On the James type constant of \(l_{p}-l_{1}\)

详细信息    查看全文

• 作者：Changsen Yang (1)
  Haiying Li (1)
  
  1. College of Mathematics and Information Science ; 46 East of Construction Road ; Xinxiang ; Henan ; 453007 ; P.R. China
  
• 关键词：46B20 ; 47H10 ; James type constant ; l p 鈭l 1 $l_{p} ; l_{1}$ space ; von Neuman ; Jordan type constant
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,080 KB
• 参考文献：1. Gao, J, Lau, KS (1991) On two classes of Banach spaces with uniform normal structure. Stud. Math. 99: pp. 41-56
  2. Clarkson, JA (1937) The von Neumann-Jordan constant for the Lebesgue space. Ann. Math. 38: pp. 114-115 CrossRef
  3. Takahashi, Y, Kato, M (2009) A simple inequality for the von Neumann-Jordan and James constants of a Banach space. J.聽Math. Anal. Appl. 359: pp. 602-609 CrossRef
  4. Wang, F (2010) On the James and von Neumann-Jordan constants in Banach spaces. Proc. Am. Math. Soc. 138: pp. 695-701 CrossRef
  5. Yang, C, Li, H (2010) An inequality between Jordan-von Neumann constant and James constant. Appl. Math. Lett. 23: pp. 277-281 CrossRef
  6. Takahashi, Y (2008) Some geometric constants of Banach spaces - a unified approach. Banach and Function Spaces II. Yokohama Publishers, Yokohama, pp. 191-220
  7. Alonso, J, Llorens-Fuster, E (2008) Geometric mean and triangles inscribed in a semicircle in Banach spaces. J. Math. Anal. Appl. 340: pp. 1271-1283 CrossRef
  8. Baronti, M, Casini, E, Papini, PL (2000) Triangles inscribed in semicircle, in Minkowski planes, and in normed spaces. J. Math. Anal. Appl. 252: pp. 124-146 CrossRef
  9. Gao, J (2006) A Pythagorean approach in Banach spaces. J. Inequal. Appl. 2006: CrossRef
  10. Yang, C, Wang, F (2006) On a new geometric constant related to the von Neumann-Jordan constant. J. Math. Anal. Appl. 324: pp. 555-565 CrossRef
  11. Dhompongsa, S, Piraisangjun, P, Saejung, S (2003) Generalised Jordan-von Neumann constants and uniform normal structure. Bull. Aust. Math. Soc. 67: pp. 225-240 CrossRef
  12. Yang, C (2013) An inequality between the James type constant and the modulus of smoothness. J. Math. Anal. Appl. 398: pp. 622-629 CrossRef
  13. Yang, C, Wang, H (2015) Two estimates for the James type constant. Ann. Funct. Anal. 6: pp. 139-147
  14. Yang, C, Wang, Y (2012) Some properties of James type constant. Appl. Math. Lett. 25: pp. 538-544 CrossRef
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

For any \(\tau\geq0\) , \(t\geq1\) and \(p\geq1\) , the exact value of the James type constant \(J_{X,t}(\tau)\) of the \(l_{p}-l_{1}\) space is investigated. As an application, the exact value of the von Neuman-Jordan type constant of the \(l_{p}-l_{1}\) space can also be obtained.