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In-Sphere Property and Reverse Inequalities for Matrix Means

Authors: 

Trung-Hoa Dinh, Tin-Yau Tam, And Bich-Khue T. Vo

Source title: 
Electronic Journal of Linear Algebra, 35: 35-41, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

The in-sphere property for matrix means is studied. It is proved that the matrix power mean satisfies in-sphere property with respect to the Hilbert-Schmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained.