## Nihonkai Mathematical Journal

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

### A refinement of the grand Furuta inequality

Masatoshi Fujii and Ritsuo Nakamoto

#### Abstract

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

**Source**

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

**Dates**

Received: 18 January 2016

Revised: 11 June 2016

First available in Project Euclid: 14 September 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.nihmj/1505419745

**Mathematical Reviews number (MathSciNet)**

MR3698245

**Zentralblatt MATH identifier**

06820451

**Subjects**

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.)

**Keywords**

Löwner--Heinz inequality Furuta inequality grand Furuta inequality

#### Citation

Fujii, Masatoshi; Nakamoto, Ritsuo. A refinement of the grand Furuta inequality. Nihonkai Math. J. 27 (2016), no. 1-2, 117--123. https://projecteuclid.org/euclid.nihmj/1505419745