On the P-property of Z and Lyapunov-like transformations on Euclidean Jordan algebras

Abstract: The P, , and properties of a linear transformation on a Euclidean Jordan algebra are generalizations of the corresponding properties of a square matrix on R n . Motivated by the equivalence of P and properties for a Z-matrix and a similar result for Lyapunov and Stein transformations on the space of real symmetric matrices , in this paper, we present two results supporting the conjecture that P and properties are equivalent for a Z-transformation on a Euclidean Jordan algebra. We show that the conjecture holds for Lyapunov-like transformations and Z-transformations satisfying an additional condition. [Copyright &y& Elsevier]