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In-Sphere Property and Reverse Inequalities for Matrix Means
Dinh et al. - 2019 - In-Sphere Property and Reverse Inequalities for Ma.pdf
Dinh et al. - 2019 - In-Sphere Property and Reverse Inequalities for Ma.pdf (92.77Kb)
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.