## Annals of Functional Analysis

- Ann. Funct. Anal.
- Volume 10, Number 4 (2019), 509-514.

### A note on the paper “Matrix inequalities for the difference between arithmetic mean and harmonic mean”

Changsen Yang, Yonghui Ren, and Haixia Zhang

#### Abstract

In this short article, we mainly give some examples to prove that the main results of Section 4 of the paper [W. S. Liao and J. Wu, Ann. Func. Anal. 6 (2015), no. 3, 191–202] are not true. Then we give the corrected matrix inequalities.

#### Article information

**Source**

Ann. Funct. Anal., Volume 10, Number 4 (2019), 509-514.

**Dates**

Received: 9 October 2018

Accepted: 31 January 2019

First available in Project Euclid: 23 October 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1571796076

**Digital Object Identifier**

doi:10.1215/20088752-2019-0009

**Mathematical Reviews number (MathSciNet)**

MR4026364

**Zentralblatt MATH identifier**

07126068

**Subjects**

Primary: 15A45: Miscellaneous inequalities involving matrices

Secondary: 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] 26E60: Means [See also 47A64]

**Keywords**

arithmetic mean harmonic mean matrix inequality Hilbert–Schmidt norm

#### Citation

Yang, Changsen; Ren, Yonghui; Zhang, Haixia. A note on the paper “Matrix inequalities for the difference between arithmetic mean and harmonic mean”. Ann. Funct. Anal. 10 (2019), no. 4, 509--514. doi:10.1215/20088752-2019-0009. https://projecteuclid.org/euclid.afa/1571796076