## Abstract

We show that Tanahashi’s argument on best possibility of the grand Furuta inequality has an additional consequence.

Show Summary Details# Another consequence of tanahashi’s argument on best possibility of the grand Furuta inequality

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*Journal of Inequalities and Applications*, 2014, Volume 2014, Number 1, Page 297

More options …# Open Mathematics

### formerly Central European Journal of Mathematics

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Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Tatsuya Koizumi / Keiichi Watanabe

We show that Tanahashi’s argument on best possibility of the grand Furuta inequality has an additional consequence.

MSC: 47A63

Keywords: Löwner-Heinz inequality; Furuta inequality; Order preserving operator inequality

[1] Ando T., Hiai F., Log majorization and complementary Golden-Thompson type inequalities, Linear Algebra Appl., 1994, 197/198, 113–131 http://dx.doi.org/10.1016/0024-3795(94)90484-7CrossrefGoogle Scholar

[2] Fujii M., Matsumoto A., Nakamoto R., A short proof of the best possibility for the grand Furuta inequality, J. Inequal. Appl., 1999, 4(4), 339–344 Web of ScienceGoogle Scholar

[3] Furuta T., A ≥ B ≥ 0 assures (B rA pB r)1/q ≥ B (p+2r)/q for r ≥ 0, p ≥ 0, q ≥ 1 with (1 + 2r)q ≥ p + 2r, Proc. Amer. Math. Soc., 1987, 101(1), 85–88 Google Scholar

[4] Furuta T., Extension of the Furuta inequality and Ando-Hiai log-majorization, Linear Algebra Appl., 1995, 219, 139–155 http://dx.doi.org/10.1016/0024-3795(93)00203-CCrossrefGoogle Scholar

[5] Heinz E., Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann., 1951, 123, 415–438 http://dx.doi.org/10.1007/BF02054965CrossrefGoogle Scholar

[6] Löwner K., Über monotone Matrixfunktionen, Math. Z., 1934, 38(1), 177–216 http://dx.doi.org/10.1007/BF01170633CrossrefGoogle Scholar

[7] Tanahashi K., Best possibility of the Furuta inequality, Proc. Amer. Math. Soc., 1996, 124(1), 141–146 http://dx.doi.org/10.1090/S0002-9939-96-03055-9CrossrefGoogle Scholar

[8] Tanahashi K., The best possibility of the grand Furuta inequality, Proc. Amer. Math. Soc., 2000, 128(2), 511–519 http://dx.doi.org/10.1090/S0002-9939-99-05261-2CrossrefGoogle Scholar

[9] Yamazaki T., Simplified proof of Tanahashi’s result on the best possibility of generalized Furuta inequality, Math. Inequal. Appl., 1999, 2(3), 473–477 Google Scholar

**Published Online**: 2012-11-21

**Published in Print**: 2013-02-01

**Citation Information: **Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-012-0061-3.

© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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Keiichi Watanabe

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