## Advances in Operator Theory

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

### The matrix power means and interpolations

Trung Hoa Dinh, Raluca Dumitru, and Jose A. Franco

#### 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**

Received: 5 January 2018

Accepted: 28 February 2018

First available in Project Euclid: 4 April 2018

**Permanent link to this document**

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

**Keywords**

Kubo-Ando means interpolation arithmetic mean geometric mean harmonic mean Heron means Heinz means power means

#### 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