The von Neumann–Jordan Constant for a Class of Day–James Spaces

Abstract

We study the von Neumann–Jordan (NJ) constant for a class of Day–James spaces, namely the lp−l1 space, as well as its dual space. In this paper, we only consider the case for p ≥ 2, since the case for 1 ≤ p ≤ 2 has been calculated. If (p−2)22(1/p-1) ≤ 1, we obtain the exact value of the NJ constant; if (p−2)22(1/p-1) > 1, we obtain a formula, from which one can determine the exact value of the NJ constant. As a byproduct, we give a partial answer to the question raised by Kato et al. (Studia Math 144:275–295, 2001).