数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (5): 1209-1220.doi: 10.1016/S0252-9602(17)30068-1

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ON A GENERALIZED GEOMETRIC CONSTANT AND SUFFICIENT CONDITIONS FOR NORMAL STRUCTURE IN BANACH SPACES

Mina DINARVAND   

  1. Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran
  • 收稿日期:2016-08-28 修回日期:2017-03-30 出版日期:2017-10-25 发布日期:2017-10-25
  • 作者简介:Mina DINARVAND,E-mail:dinarvand mina@yahoo.com

ON A GENERALIZED GEOMETRIC CONSTANT AND SUFFICIENT CONDITIONS FOR NORMAL STRUCTURE IN BANACH SPACES

Mina DINARVAND   

  1. Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran
  • Received:2016-08-28 Revised:2017-03-30 Online:2017-10-25 Published:2017-10-25

摘要:

In this paper,we introduce a new geometric constant CNJ(p)(a,X) of a Banach space X,which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant.Subsequently,we present several sufficient conditions for normal structure of a Banach space in terms of this new constant,the generalized James constant,the generalized García-Falset coefficient and the coefficient of weak orthogonality of Sims.Our main results of the paper generalize some known results in the recent literature.

关键词: uniform normal structure, generalized Garcí, a-Falset coefficient, coefficient of weak orthogonality, constant CNJ(p)(a,X), generalized James constant

Abstract:

In this paper,we introduce a new geometric constant CNJ(p)(a,X) of a Banach space X,which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant.Subsequently,we present several sufficient conditions for normal structure of a Banach space in terms of this new constant,the generalized James constant,the generalized García-Falset coefficient and the coefficient of weak orthogonality of Sims.Our main results of the paper generalize some known results in the recent literature.

Key words: uniform normal structure, generalized Garcí, a-Falset coefficient, coefficient of weak orthogonality, constant CNJ(p)(a,X), generalized James constant