Characterizations of Jordan *-isomorphisms of C^* -algebras by Schatten p -norm of Kubo–Ando means

We consider three operations on the positive definite cones of C^* -algebras which are Schatten p -norm of various versions of the quantum Rényi relative entropy. The main results concern how Jordan * -isomorphisms between C^* -algebras can be characterized by the preservation of the Schatten p -norms of those operations.