Extremal structure of absolute normalized norms on R2R2 and the James constant

We denote by AN2 the set of all absolute normalized norms on R2R2. The set AN2 has a convex structure with respect to the usual operation. In this paper we calculate the James constant of (R2,‖·‖)(R2,‖·‖) when ∥·∥ is an extreme point of AN2.