T. H. Dinh, A. T. Nguyen, D. A. N. Nguyen, H. T. L. Truong, “An unexpected AGM-type inequality and a new characterization of operator monotone functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2026, Number 2,Pages <nobr>15

An unexpected AGM-type inequality and a new characterization of operator monotone functions

T. H. Dinh^a, A. T. Nguyen^bc, D. A. N. Nguyen^bcd, H. T. L. Truong^bce

^a Troy University, Troy, Alabama, 36082 USA
^b University of Science, Ho Chi Minh City, Vietnam
^c Vietnam National University, Ho Chi Minh City, Vietnam
^d Hue University, Hue, Vietnam
^e FPT University, Danang, Vietnam

Abstract: In this paper, a new arithmetic-geometric mean type inequality for positive definite matrices is established. As an application, the new inequality is used to characterize operator monotone functions.

Keywords: operator monotone function, AGM inequality, characterization of operator monotonicity, positive definite matrix.

UDC: 517

Received: 12.09.2024
Revised: 19.09.2024
Accepted: 26.09.2024

DOI: 10.26907/0021-3446-2026-2-15-24