Some trace inequalities for matrix means
© Zou and Peng 2016
Received: 8 September 2016
Accepted: 9 November 2016
Published: 17 November 2016
In this short note, we present some trace inequalities for matrix means. Our results are generalizations of the ones shown by Bhatia, Lim, and Yamazaki.
Keywordspositive definite matrices matrix means trace inequalities
2 Main results
In this section, we first give a trace inequality, which is similar to inequality (1.1). To do this, we need the following lemmas.
This is the Hölder inequality of unitary invariant norms for matrices. For more information on this inequality and its applications the reader is referred to  and the references therein.
The authors wish to express their heartfelt thanks to the referees and Professor Sin E Takahasi for their detailed and helpful suggestions for revising the manuscript. This research was supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ1501004).
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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