Matrix inequalities involving a positive linear map
Chi-Kwong Li, Roy Mathias · Linear and Multilinear Algebra · 1996
Let A be a Hermitian matrix, let Φ be a normalized positive linear map and let f be a continuous real valued function. Real constants α and β such that are determined. If f is matrix convex then β can be taken to be 1. A unified approach is proposed so that the problem of determining α and β is reduced to solving a single variable convex minimization problem. As an illustration, the results are applied to the power functions.