In-sphere property and reverse inequalities for matrix means

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Trung Hoa Dinh
Tin-Yau Tam
Bich Khue T Vo


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.

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