Nonlinear mappings preserving product \(XY+YX^\ast\) on factor von Neumann algebras (Q1938690)

Let \(\mathcal A\) and \(\mathcal B\) be two factor von Neumann algebras and let \(\phi: \mathcal A \to \mathcal B\) be a bijective mapping. The authors of the present paper show that \(\phi\) satisfies the condition \[ \phi (AB+BA^*)= \phi (A) \phi (B) + \phi (B) \phi(A)^* \] for all \(A,B \in \mathcal A\) if and only if \(\phi\) is a *-ring isomorphism.