For a non-trivial Banach space X, let J（X）,CNj（X）,C（P）NJ（X） respectively stand for the James constant, the yon Neumann-Jordan constant and the generalized yon Neumann-Jordan constant receatly inroduced by Cui ...For a non-trivial Banach space X, let J（X）,CNj（X）,C（P）NJ（X） respectively stand for the James constant, the yon Neumann-Jordan constant and the generalized yon Neumann-Jordan constant receatly inroduced by Cui et al. In this paper, we discuss the relatioa between the James and the generalized yon Neumann-Jordan constants, and establish an inequality between them： C（P）NJ（X） ≤ J（X） with p 〉 2, which covers the well-known inequality CNJ（X） ≤ J（X）. We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al.展开更多
We shall introduce a new geometric constant A（X） of a Banach space X, which is closely related to the modulus of smoothness px （T）, and investigate it in relation with the constant As （X） by Baronti et al., the ...We shall introduce a new geometric constant A（X） of a Banach space X, which is closely related to the modulus of smoothness px （T）, and investigate it in relation with the constant As （X） by Baronti et al., the von Neumann-Jordan constant CNj（X） and the James constant J（X）. A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11271112 and 11201127)Innovation Scientists and Technicians Troop Construction Projects of He’nan Province(Grant No.114200510011,C20150027)
文摘For a non-trivial Banach space X, let J（X）,CNj（X）,C（P）NJ（X） respectively stand for the James constant, the yon Neumann-Jordan constant and the generalized yon Neumann-Jordan constant receatly inroduced by Cui et al. In this paper, we discuss the relatioa between the James and the generalized yon Neumann-Jordan constants, and establish an inequality between them： C（P）NJ（X） ≤ J（X） with p 〉 2, which covers the well-known inequality CNJ（X） ≤ J（X）. We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al.
基金The second author is supported in part by Grant-in-Aid for Scientific Research,Japan Society for the Promotionof Science(Grant No.23540216)
文摘We shall introduce a new geometric constant A（X） of a Banach space X, which is closely related to the modulus of smoothness px （T）, and investigate it in relation with the constant As （X） by Baronti et al., the von Neumann-Jordan constant CNj（X） and the James constant J（X）. A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved.
