Upper and lower bounds for the difference between the weighted arithmetic and harmonic operator means

Abstract

In this paper we establish some new upper and lower bounds for the difference between the weighted arithmetic and harmonic operator means under various assumption for the positive invertible operators A, B. Some applications when A, B are bounded above and below by positive constants are given as well.

Keywords

• Young’s inequality
• convex functions
• arithmetic mean-Harmonic mean inequality
• operator means
• operator inequalities