Multiplicatively spectrum-preserving maps on $C^{*}$-algebras (2404.04563v1)

Abstract: We study surjective maps between the sets of all self-adjoint elements of unital $C^*$-algebras which satisfy the multiplicatively spectrum-preserving property. We show that such maps are characterized by Jordan isomorphisms and central symmetries. This is an answer to a problem posed by Moln\'ar.