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

Volume 217 / 2013

Bartosz Kołodziejek Studia Mathematica 217 (2013), 1-17 MSC: Primary 62H05. DOI: 10.4064/sm217-1-1


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.


  • Bartosz KołodziejekFaculty of Mathematics and Information Science
    Warsaw University of Technology
    Pl. Politechniki 1
    00-661 Warszawa, Poland

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