A convex operator function
The author shows that the inversion function \(f(x)=x^{-1}\) on a the positive invertible elements of a C *-algebra is convex in the sense that \(f(\lambda x+(1-\lambda)y)\leq \lambda f(x)+(1-\lambda)f(y)\) for \(0\leq \lambda \leq 1\). The same theorem appears in {\S} 1.3.11 of \textit{G. K. Pedersen}'s book, C *-algebras and their automorphism groups (1979; Zbl 0416.46043).
positive invertible elements of a C *-algebra
scientific article; zbMATH DE number 4069642