Extreme points and optimal measures

We provide a new and more efficient proof of our earlier result that every 2×2 Toeplitz matrix M has a representing measure μ that is optimal in the sense that ‖μ‖=‖M‖S, the norm of M as a Schur multiplier. This result is seen to follow from some elementary observations about extreme points in the unit ball of trigonometric trinomials. We also discuss the complete characterization of such extreme points.