Year 2020, Volume 49 , Issue 5, Pages 1744 - 1752 2020-10-06

On the Pólya-Szegö operator inequality

Trung Hoa DİNH [1] , Hamid Reza MORADI [2] , Mohammad SABABHEH [3]


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.

**************************************************************************************************************************

**************************************************************************************************************************

Operator inequality, operator mean, positive linear map, Pólya-Szegö inequality, operator monotone functions
  • [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 .
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-6303-1427
Author: Trung Hoa DİNH
Institution: Troy University
Country: United States


Orcid: 0000-0002-0233-0455
Author: Hamid Reza MORADI
Institution: Payame Noor University
Country: Iran


Orcid: 0000-0002-1321-2702
Author: Mohammad SABABHEH (Primary Author)
Institution: Princess Sumaya University for Technology
Country: Jordan


Dates

Publication Date : October 6, 2020

Bibtex @research article { hujms547158, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1744 - 1752}, doi = {10.15672/hujms.547158}, title = {On the Pólya-Szegö operator inequality}, key = {cite}, author = {Di̇nh, Trung Hoa and Moradı, Hamid Reza and Sababheh, Mohammad} }
APA Di̇nh, T , Moradı, H , Sababheh, M . (2020). On the Pólya-Szegö operator inequality . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1744-1752 . DOI: 10.15672/hujms.547158
MLA Di̇nh, T , Moradı, H , Sababheh, M . "On the Pólya-Szegö operator inequality" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1744-1752 <https://dergipark.org.tr/en/pub/hujms/issue/57199/547158>
Chicago Di̇nh, T , Moradı, H , Sababheh, M . "On the Pólya-Szegö operator inequality". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1744-1752
RIS TY - JOUR T1 - On the Pólya-Szegö operator inequality AU - Trung Hoa Di̇nh , Hamid Reza Moradı , Mohammad Sababheh Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.547158 DO - 10.15672/hujms.547158 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1744 EP - 1752 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.547158 UR - https://doi.org/10.15672/hujms.547158 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On the Pólya-Szegö operator inequality %A Trung Hoa Di̇nh , Hamid Reza Moradı , Mohammad Sababheh %T On the Pólya-Szegö operator inequality %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.547158 %U 10.15672/hujms.547158
ISNAD Di̇nh, Trung Hoa , Moradı, Hamid Reza , Sababheh, Mohammad . "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
AMA Di̇nh T , Moradı H , Sababheh M . On the Pólya-Szegö operator inequality. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1744-1752.
Vancouver Di̇nh T , Moradı H , Sababheh M . On the Pólya-Szegö operator inequality. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1744-1752.