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), 147-160]. The main tool is a new solution of the Olkin-Baker functional equation on symmetric cones, under the assumption of continuity of respective functions. It was possible thanks to the use of Gleason's theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-1-1,
author = {Bartosz Ko\l odziejek},
title = {The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {1-17},
zbl = {06207624},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-1-1}
}
Bartosz Kołodziejek. The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem. Studia Mathematica, Tome 215 (2013) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-1-1/