Norm-Additive Maps on the Positive Definite Cone of a C*-Algebra

In this paper, we determine the structure of Schatten p-norm additive maps on the set of positive invertible elements of a C*-algebra carrying a faithful normalized trace. It turns out that any such transformation originates from a Jordan *-isomorphism of the underlying C*-algebra. In fact, our result can be viewed as a characterization of that sort of isomorphisms.