A REPRESENTATION THEOREM FOR LYAPUNOV-LIKE TRANSFORMATIONS ON EUCLIDEAN JORDAN ALGEBRAS
Jiyuan Tao, M. Seetharama Gowda · International Game Theory Review · 2013
A Lyapunov-like (linear) transformation L on a Euclidean Jordan algebra V is defined by the condition [Formula: see text]where K is the symmetric cone of V. In this paper, we give an elementary proof (avoiding Lie algebraic ideas and results) of the fact that Lyapunov-like transformations on V are of the form La+ D, where a ∈ V, D is a derivation, and La(x) = a ◦ x for all x ∈ V.