ON A GENERALIZED JORDAN-VON NEUMANN TYPE CONSTANT AND NORMAL STRUCTURE

In this paper, we introduce a new geometric constant C--infinity((p)) (a,X) , which is closely related to the generalized Jordan-von Neumann type constant. We show that 2 and (a+2)(p)/2(p-2) (2(p) + a(p)) are the upper and lower bound for C--infinity((p)) (a,X) , respectively. Moreover, we obtain that C--infinity((p)) (a, X) = C--infinity((p)), (a, X-similar to) , where X-similar to is the ultrapower space of X . Subsequently, we give some sufficient conditions for normal structure of a Banach space with different constants, such as the generalized James constant, Dom & imath;nguez-Benavides coefficient and the coefficient of weak orthogonality.