Inequalities for arithmetic–geometric–harmonic means of sector matrices

We provide upper and lower bounds for the weighted arithmetic mean, geometric mean and harmonic mean of a set of sector matrices. It generalizes Sagae and Tanabe's result in [Linear Multilinear Algebra. 1994;37:279–282] to multiple sector matrices. As an application of the bounds, we present inequalities for singular values, determinants and unitarily invariant norms.