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Year 2020, Volume: 49 Issue: 5, 1744 - 1752, 06.10.2020
https://doi.org/10.15672/hujms.547158

Abstract

References

  • [1] T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26, 203–241, 1979.
  • [2] T. Ando and F. Hiai, Operator log-convex functions and operator means, Math. Ann. 350 (3), 611–630, 2011.
  • [3] J.C. Bourin, E.Y. Lee, M. Fujii and Y. Seo, A matrix reverse Hölder inequality, Linear Algebra Appl. 431 (11), 2154–2159, 2009.
  • [4] M. Fujii, S. Izumino, R. Nakamoto and Y. Seo, Operator inequalities related to Cauchy-Schwarz and Hölder-McCarthy inequalities, Nihonkai Math. J. 8, 117–122, 1997.
  • [5] J.I. Fujii, M. Nakamura, J. Pečarić and Y. Seo, Bounds for the ratio and difference between parallel sum and series via Mond-Pečarić method, Math. Inequal. Appl. 9 (4), 749–759, 2006.
  • [6] S. Furichi, H.R. Moradi and M. Sababheh, New sharp inequalities for operator means, Linear Multilinear Algebra, 67, 1567–1578, 2019.
  • [7] M.B. Ghaemi and V. Kaleibary, Some inequalities involving operator monotone func- tions and operator means, Math. Inequal. Appl. 19 (2), 757–764, 2016.
  • [8] I. Gumus, H.R. Moradi and M. Sababheh, More accurate operator means inequalities, J. Math. Anal. Appl. 465, 267–280, 2018.
  • [9] T.H. Dinh, T.H.B. Du and M.T. Ho On some matrix mean inequalities with Kan- torovich constant, Sci. Math. Jpn. 80 (2), 139–151, 2017.
  • [10] T.H. Dinh, M.S. Moslehian, C. Conde and P. Zhang, An extension of the Pólya-Szegö operator inequality, Expo. Math. 35 (2), 212–220, 2017.
  • [11] F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246, 205–224, 1980.
  • [12] E.Y. Lee, A matrix reverse Cauchy-Schwarz inequality, Linear Algebra Appl. 430, 805–810, 2009.
  • [13] T. Furuta, J. Mićić, J. Pečarić and Y. Seo, Mond–Pečarić method in operator inequal- ities, Element, Zagreb, 2005.
  • [14] W. Specht, Zur Theorie der elementaren Mittel, Math. Z. 74, 91–98, 1960 .

On the Pólya-Szegö operator inequality

Year 2020, Volume: 49 Issue: 5, 1744 - 1752, 06.10.2020
https://doi.org/10.15672/hujms.547158

Abstract

In this paper, we present generalized Pólya-Szegö type inequalities for positive invertible operators on a Hilbert space for arbitrary operator means between the arithmetic and the harmonic means. As applications, we present operator Grüss, Diaz–Metcalf, and Klamkin–McLenaghan inequalities.

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References

  • [1] T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26, 203–241, 1979.
  • [2] T. Ando and F. Hiai, Operator log-convex functions and operator means, Math. Ann. 350 (3), 611–630, 2011.
  • [3] J.C. Bourin, E.Y. Lee, M. Fujii and Y. Seo, A matrix reverse Hölder inequality, Linear Algebra Appl. 431 (11), 2154–2159, 2009.
  • [4] M. Fujii, S. Izumino, R. Nakamoto and Y. Seo, Operator inequalities related to Cauchy-Schwarz and Hölder-McCarthy inequalities, Nihonkai Math. J. 8, 117–122, 1997.
  • [5] J.I. Fujii, M. Nakamura, J. Pečarić and Y. Seo, Bounds for the ratio and difference between parallel sum and series via Mond-Pečarić method, Math. Inequal. Appl. 9 (4), 749–759, 2006.
  • [6] S. Furichi, H.R. Moradi and M. Sababheh, New sharp inequalities for operator means, Linear Multilinear Algebra, 67, 1567–1578, 2019.
  • [7] M.B. Ghaemi and V. Kaleibary, Some inequalities involving operator monotone func- tions and operator means, Math. Inequal. Appl. 19 (2), 757–764, 2016.
  • [8] I. Gumus, H.R. Moradi and M. Sababheh, More accurate operator means inequalities, J. Math. Anal. Appl. 465, 267–280, 2018.
  • [9] T.H. Dinh, T.H.B. Du and M.T. Ho On some matrix mean inequalities with Kan- torovich constant, Sci. Math. Jpn. 80 (2), 139–151, 2017.
  • [10] T.H. Dinh, M.S. Moslehian, C. Conde and P. Zhang, An extension of the Pólya-Szegö operator inequality, Expo. Math. 35 (2), 212–220, 2017.
  • [11] F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246, 205–224, 1980.
  • [12] E.Y. Lee, A matrix reverse Cauchy-Schwarz inequality, Linear Algebra Appl. 430, 805–810, 2009.
  • [13] T. Furuta, J. Mićić, J. Pečarić and Y. Seo, Mond–Pečarić method in operator inequal- ities, Element, Zagreb, 2005.
  • [14] W. Specht, Zur Theorie der elementaren Mittel, Math. Z. 74, 91–98, 1960 .
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Trung Hoa Dinh This is me 0000-0001-6303-1427

Hamid Reza Moradı 0000-0002-0233-0455

Mohammad Sababheh 0000-0002-1321-2702

Publication Date October 6, 2020
Published in Issue Year 2020 Volume: 49 Issue: 5

Cite

APA Dinh, T. H., Moradı, H. R., & Sababheh, M. (2020). On the Pólya-Szegö operator inequality. Hacettepe Journal of Mathematics and Statistics, 49(5), 1744-1752. https://doi.org/10.15672/hujms.547158
AMA Dinh TH, Moradı HR, Sababheh M. On the Pólya-Szegö operator inequality. Hacettepe Journal of Mathematics and Statistics. October 2020;49(5):1744-1752. doi:10.15672/hujms.547158
Chicago Dinh, Trung Hoa, Hamid Reza Moradı, and Mohammad Sababheh. “On the Pólya-Szegö Operator Inequality”. Hacettepe Journal of Mathematics and Statistics 49, no. 5 (October 2020): 1744-52. https://doi.org/10.15672/hujms.547158.
EndNote Dinh TH, Moradı HR, Sababheh M (October 1, 2020) On the Pólya-Szegö operator inequality. Hacettepe Journal of Mathematics and Statistics 49 5 1744–1752.
IEEE T. H. Dinh, H. R. Moradı, and M. Sababheh, “On the Pólya-Szegö operator inequality”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 5, pp. 1744–1752, 2020, doi: 10.15672/hujms.547158.
ISNAD Dinh, Trung Hoa et al. “On the Pólya-Szegö Operator Inequality”. Hacettepe Journal of Mathematics and Statistics 49/5 (October 2020), 1744-1752. https://doi.org/10.15672/hujms.547158.
JAMA Dinh TH, Moradı HR, Sababheh M. On the Pólya-Szegö operator inequality. Hacettepe Journal of Mathematics and Statistics. 2020;49:1744–1752.
MLA Dinh, Trung Hoa et al. “On the Pólya-Szegö Operator Inequality”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 5, 2020, pp. 1744-52, doi:10.15672/hujms.547158.
Vancouver Dinh TH, Moradı HR, Sababheh M. On the Pólya-Szegö operator inequality. Hacettepe Journal of Mathematics and Statistics. 2020;49(5):1744-52.