Norm-Additive Maps on the Positive Definite Cone of a $$\varvec{C^{*}}$$-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.