Nihonkai Mathematical Journal

Equivalence relations among some inequalities on operator means

Shuhei Wada and Takeaki Yamazaki

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We will consider some inequalities on operator means for more than three operators, for instance, ALM and BMP geometric means will be considered. Moreover, log-Euclidean and logarithmic means for several operators will be treated.


This work is based on research supported by the INOUE ENRYO Memorial Foundation for Promoting Sciences.

Article information

Nihonkai Math. J., Volume 27, Number 1-2 (2016), 1-15.

Received: 6 August 2015
Revised: 10 February 2016
First available in Project Euclid: 14 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A64: Operator means, shorted operators, etc.
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 47A63: Operator inequalities

positive definite operators operator mean ALM mean BMP mean log-Euclidean mean Karcher mean power mean logarithmic mean


Wada, Shuhei; Yamazaki, Takeaki. Equivalence relations among some inequalities on operator means. Nihonkai Math. J. 27 (2016), no. 1-2, 1--15.

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