The von Neumann-Jordan constant, weak orthogonality and normal structure in Banach spaces

Abstract

We give some sufficient conditions for normal structure in terms of the von Neumann-Jordan constant, the James constant and the weak orthogonality coefficient introduced by B. Sims. In the rest of the paper, the von Neumann-Jordan constant and the James constant for the Bynum space ℓ 2 , ∞ \ell _{2,\infty } are computed, and are used to show that our results are sharp.