Nihonkai Mathematical Journal

A refinement of the grand Furuta inequality

Masatoshi Fujii and Ritsuo Nakamoto

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A refinement of the Löwner--Heinz inequality has been discussed by Moslehian--Najafi. In the preceding paper, we improved it and extended to the Furuta inequality. In this note, we give a further extension for the grand Furuta inequality. We also discuss it for operator means. A refinement of the arithmetic-geometric mean inequality is obtained.

Article information

Nihonkai Math. J., Volume 27, Number 1-2 (2016), 117-123.

Received: 18 January 2016
Revised: 11 June 2016
First available in Project Euclid: 14 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 47A30: Norms (inequalities, more than one norm, etc.)

Löwner--Heinz inequality Furuta inequality grand Furuta inequality


Fujii, Masatoshi; Nakamoto, Ritsuo. A refinement of the grand Furuta inequality. Nihonkai Math. J. 27 (2016), no. 1-2, 117--123.

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