In-sphere property of matrix means, matrix Heinz mean, matrix power mean, unitarily invariant norms
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.
Dinh, Trung Hoa; Tam, Tin-Yau; and Vo, Bich Khue T.
"In-sphere property and reverse inequalities for matrix means",
Electronic Journal of Linear Algebra,
Volume 35, pp. 35-41.