On the Wiener-Hopf compactification of a symmetric cone

Abstract

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