Generalize the mean inequalities for sector matrices

In this paper, we present some mean inequalities for sector matrices involv- ing positive linear maps which generalize the results of Chansangiam. Moreover, weextend the famous mean inequalities to sector matrix case. We obtain several inequal- ities including a matrix inequality, singular value inequalities, determinant inequalities and unitarily invariant norm inequalities.

Keywords:

Accretive operator , Operator monotone , Operator mean , Inequality