Nihonkai Mathematical Journal

A refinement of the grand Furuta inequality

Masatoshi Fujii and Ritsuo Nakamoto

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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


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References

  • T. Ando and F. Hiai, Log majorization and complementary Golden-Thompson type inequalities, Linear Algebra Appl. 197/198 (1994), 113–131.
  • M. Fujii, Furuta's inequality and its mean theoretic approach, J. Operator Theory 23 (1990), 67–72.
  • M. Fujii, Y.O. Kim and R. Nakamoto, A characterization of convex functions and its application to operator monotone functions, Banach J. Math. Anal. 8 (2014), 118–123.
  • M. Fujii, M. S. Moslehian, F. Najafi and R. Nakamoto, Estimates of operator convex and operator monotone functions on bounded intervals, Hokkaido Math. J., to appear.
  • T. Furuta, $A \geq B \geq 0$ assures $(B^rA^pB^r)^{1/q} \geq B^{(p+2r)/q}$ for $r \geq 0,\ p \geq 0,\ q \geq 1$ with $(1 + 2r)q \geq p + 2r$, Proc. Amer. Math. Soc. 101 (1987), 85–88.
  • T. Furuta, Elementary proof of an order preserving inequality, Proc. Japan Acad. 65 (1989), 126.
  • T. Furuta, Precise lower bound of $f(A)-f(B)$ for $A>B>0$ and non-constant operator monotone function $f$ on $[0, \infty)$, J. Math. Inequal. 9 (2015), 47–52.
  • E. Kamei, A satellite to Furuta's inequality, Math. Japon. 33 (1988), 883–886.
  • M.S. Moslehian and H. Najafi, An extension of the Löwner–Heinz inequality, Linear Algebra Appl. 437 (2012), 2359–2365.
  • K. Tanahashi, Best possibility of the Furuta inequality, Proc. Amer. Math. Soc. 124 (1996), 141–146.