Inequalities characterizing linear-multiplicative functionals (Q492613)

Let \(A\) be a unital algebra over the field of real line \(\mathbb{R}\). The author proves that a nonconstant mapping \(\phi: A \to \mathbb{R}\) is midpoint concave (i.e., \(\phi\left(\frac{f+g}{2}\right) \leq \frac{\phi(f)+\phi(g)}{2}\) for all \(f, g\in A\)) and supermultiplicative (i.e., \(\phi(fg)\geq \phi(f)\phi(g)\) for \(f, g\in A\)) if and only if it is linear and multiplicative. He then applies his result to determine all Jensen concave and supermultiplicative operators \(T: C(X) \to C(Y)\), where \(X\) and \(Y\) are compact Hausdorff spaces.