### The matrix power means and interpolations

#### Abstract

‎It is well-known that the Heron mean is a linear interpolation between the arithmetic and the geometric means while the matrix power mean $P_t(A,B):= A^{1/2}\left(\frac{I+(A^{-1/2}BA^{-1/2})^t}{2}\right)^{1/t}A^{1/2}$ interpolates between the harmonic‎, ‎the geometric‎, ‎and the arithmetic means‎. ‎In this article‎, ‎we establish several comparisons between the matrix power mean‎, ‎the Heron mean‎, ‎and the Heinz mean‎. ‎Therefore‎, ‎we have a deeper understanding about the distribution of these matrix means‎.

#### Article information

Source
Adv. Oper. Theory, Volume 3, Number 3 (2018), 647-654.

Dates
Accepted: 28 February 2018
First available in Project Euclid: 4 April 2018

https://projecteuclid.org/euclid.aot/1522807282

Digital Object Identifier
doi:10.15352/aot.1801-1288

Mathematical Reviews number (MathSciNet)
MR3795106

Zentralblatt MATH identifier
06902458

Subjects
Primary: 47A63: Operator inequalities
Secondary: 47A64‎ ‎47A56

#### Citation

Dinh, Trung Hoa; Dumitru, ‎Raluca; ‎Franco, Jose A‎. The matrix power means and interpolations. Adv. Oper. Theory 3 (2018), no. 3, 647--654. doi:10.15352/aot.1801-1288. https://projecteuclid.org/euclid.aot/1522807282

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