On James and Jordan–von Neumann constants and the normal structure coefficient of Banach spaces

By Mikio Kato, Lech Maligranda, Y. Takahashi. 2001

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On a new geometric constant related to the von Neumann–Jordan constant (2006, background): “An equivalent definition of the NJ constant is found in [13] as the following form: CNJ(X) = sup {‖x + y‖2 + ‖x − y‖2 2(‖x‖2 + ‖y‖2) : x ∈ SX, y ∈ BX } .”
Wheeling around von Neumann-Jordan constant in Banach spaces (2008, background): “On the contrary, the value on a space is in general different from that on its dual for the constants J(X) [12] and CZ(X) [1].”
On James and von Neumann–Jordan constants and sufficient conditions for the fixed point property (2006, background): “Since CNJ(X∗)= CNJ(X) [12], it suffices to prove only that X has weak normal structure if CNJ(X) < (1 + √ 3)/2.”