Some characterizations of cone preserving Z-transformations

초록

Given a proper cone K in a finite dimensional real Hilbert space H, we present some results characterizing (Formula presented.)-transformations that keep K invariant. We show for example, that when K is irreducible, nonnegative multiples of the identity transformation are the only such transformations. And when K is reducible, they become ‘nonnegative diagonal’ transformations. We apply these results to symmetric cones in Euclidean Jordan algebras, and, in particular, obtain conditions on the Lyapunov transformation (Formula presented.) and the Stein transformation (Formula presented.) that keep the semidefinite cone invariant. © 2017 Springer Science+Business Media New York

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