The converse of the Loewner–Heinz inequality via perspective

Abstract

The Loewner–Heinz inequality is not only the most essential one in operator theory, but also a fundamental tool for treating operator inequalities. The aim of this paper is to investigate the converse of the Loewner–Heinz inequality in the view point of perspective and generalized perspective of operator monotone and multiplicative functions. Indeed, we give perspective inequalities equivalent to the Loewner–Heinz inequality.

Keywords:

• Operator monotone function
• operator mean
• Loewner–Heinz inequality
• perspective function

AMS Subject Classifications:

• Primary: 47A63
• Secondary: 46L05
• 46L60
• 81T05

Notes

No potential conflict of interest was reported by the authors.