On the Wiener-Hopf compactification of a symmetric cone

Abstract

Let V be a finite dimensional real Euclidean Jordan algebra with the identity element 1. Let Q be the closed convex cone of squares. We show that the WienerHopf compactification of Q is the interval {x ∈ V : −1 ≤ x ≤ 1}. As a consequence, we deduce that the K-groups of the Wiener-Hopf C * -algebra associated to Q are trivial.