Another consequence of tanahashi’s argument on best possibility of the grand Furuta inequality

Tatsuya Koizumi; Keiichi Watanabe

Open Mathematics (2013)

  • Volume: 11, Issue: 2, page 368-375
  • ISSN: 2391-5455

Abstract

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

How to cite

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Tatsuya Koizumi, and Keiichi Watanabe. "Another consequence of tanahashi’s argument on best possibility of the grand Furuta inequality." Open Mathematics 11.2 (2013): 368-375. <http://eudml.org/doc/269150>.

@article{TatsuyaKoizumi2013,
abstract = {We show that Tanahashi’s argument on best possibility of the grand Furuta inequality has an additional consequence.},
author = {Tatsuya Koizumi, Keiichi Watanabe},
journal = {Open Mathematics},
keywords = {Löwner-Heinz inequality; Furuta inequality; Order preserving operator inequality; order preserving operator inequality},
language = {eng},
number = {2},
pages = {368-375},
title = {Another consequence of tanahashi’s argument on best possibility of the grand Furuta inequality},
url = {http://eudml.org/doc/269150},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Tatsuya Koizumi
AU - Keiichi Watanabe
TI - Another consequence of tanahashi’s argument on best possibility of the grand Furuta inequality
JO - Open Mathematics
PY - 2013
VL - 11
IS - 2
SP - 368
EP - 375
AB - We show that Tanahashi’s argument on best possibility of the grand Furuta inequality has an additional consequence.
LA - eng
KW - Löwner-Heinz inequality; Furuta inequality; Order preserving operator inequality; order preserving operator inequality
UR - http://eudml.org/doc/269150
ER -

References

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  1. [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)90484-7 Zbl0793.15011
  2. [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 Zbl0949.47015
  3. [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 
  4. [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-C 
  5. [5] Heinz E., Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann., 1951, 123, 415–438 http://dx.doi.org/10.1007/BF02054965 Zbl0043.32603
  6. [6] Löwner K., Über monotone Matrixfunktionen, Math. Z., 1934, 38(1), 177–216 http://dx.doi.org/10.1007/BF01170633 Zbl0008.11301
  7. [7] Tanahashi K., Best possibility of the Furuta inequality, Proc. Amer. Math. Soc., 1996, 124(1), 141–146 http://dx.doi.org/10.1090/S0002-9939-96-03055-9 Zbl0841.47012
  8. [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/S0002-9939-99-05261-2 Zbl0943.47016
  9. [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 Zbl0938.47015

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