Abstract
For positive definite matrices A and B, the Kubo-Ando matrix power mean is defined as In this paper, for , we show that if one of the following inequalities holds for any positive definite matrices A and B, then the function f is operator monotone on We also study the inverse problem for non-Kubo-Ando matrix power means with the powers 1/2 and 2. As a consequence, we establish new charaterizations of operator monotone functions with the non-Kubo-Ando matrix power means.
Acknowledgments
The authors are very grateful to Prof. Mikael de la Salle for useful discussions.
Disclosure statement
No potential conflict of interest was reported by the authors.