An Unexpected AGM-Type Inequality and a New Characterization of Operator Monotone Functions | Synapse
May 28, 2026
An Unexpected AGM-Type Inequality and a New Characterization of Operator Monotone Functions
Key Points
The aim is to establish a new inequality related to the arithmetic-geometric mean for positive definite matrices and apply it to classify operator monotone functions.
Developed a new arithmetic-geometric mean type inequality.
Applied the inequality to characterize operator monotone functions.
Demonstrated the existence of a new inequality for positive definite matrices.
Provided a characterization of operator monotone functions using the inequality.
Abstract
In this paper, we establish a new arithmetic-geometric mean type inequality for positive definite matrices. As an application, we use the new inequality to characterize operator monotone functions.