On the Lawson–Lim means and Karcher mean for positive invertible operators

Abstract

Abstract This note aims to generalize the reverse weighted arithmetic–geometric mean inequality of n positive invertible operators due to Lawson and Lim. In addition, we make comparisons between the weighted Karcher mean and Lawson–Lim geometric mean for higher powers.

Keywords

• Karcher mean
• Lawson–Lim geometric mean
• Ando–Li–Mathias geometric mean
• Kantorovich constant