The Lukacs–Olkin–Rubin theorem on symmetric cones through Gleason's theorem

Abstract

We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than $2$. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka–Wesołowski, Studia Math. 152 (2002), 147