Skip to main content
SpringerLink
Log in

Some Hadamard product inequalities for accretive matrices

  • Original Paper
  • Published:
Advances in Operator Theory Aims and scope Submit manuscript

Abstract

In this paper, we obtain some new matrix inequalities involving Hadamard product. Also, some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps, and matrix concave functions are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

Not applicable.

References

  1. Ando, T.: Concavity of certain maps on positive definite matrices and applications to Hadamard products. Linear Algebra Appl. 26, 203–241 (1979)

    Article  MathSciNet  Google Scholar 

  2. Bedrani, Y., Kittaneh, F., Sababeh, M.: From positive to accretive matrices. Positivity 25, 1601–1629 (2021)

    Article  MathSciNet  Google Scholar 

  3. Bedrani, Y., Kittaneh, F., Sababeh, M.: Numerical radii of accretive matrices. Linear Multilinear Algebra 69, 957–970 (2021)

    Article  MathSciNet  Google Scholar 

  4. Bedrani, Y., Kittaneh, F., Sababeh, M.: On the weighted geometric mean of accretive matrices. Ann. Funct. Anal. 12, Article 2 (2021)

    Article  MathSciNet  Google Scholar 

  5. Bedrani, Y., Kittaneh, F., Sababeh, M.: Accretive matrices and matrix convex functions. Results Math. 77, Article 52 (2022)

    Article  MathSciNet  Google Scholar 

  6. Bhatia, R.: Positive Definite Matrices. Princeton University Press, Princeton (2007)

    Google Scholar 

  7. Chansangiam, P., Hemchote, P., Pantaragphong, P.: Inequalities for Kronecker products and Hadamard product of positive definite matrices. Sci. Asia 35, 106–110 (2009)

    Article  Google Scholar 

  8. Choi, D., Tam, T., Zhang, P.: Extension of Fischer’s inequality. Linear Algebra Appl. 569, 311–322 (2019)

    Article  MathSciNet  Google Scholar 

  9. Drury, S.: Principal powers of matrices with positive definite real part. Linear Multilinear Algebra 63, 296–301 (2015)

    Article  MathSciNet  Google Scholar 

  10. Furuichi, Sh., Moradi, H.R., Sababeh, M.: New sharp inequalities for operator means. Linear Multilinear Algebra 67, 1567–1578 (2019)

    Article  MathSciNet  Google Scholar 

  11. Gueridi, D., Kittaneh, F.: Inequalities for the Kronecker product of matrices. Ann. Funct. Anal. 13, 50 (2022)

    Article  MathSciNet  Google Scholar 

  12. Gǔmǔs, I.H., Moradi, H.R., Sababeh, M.: More accurate operator means inequalities. J. Math. Anal. Appl. 465, 267–280 (2018)

    Article  MathSciNet  Google Scholar 

  13. Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, New York (1991)

    Book  Google Scholar 

  14. Khosravi, M., Sheikhhosseini, A., Malekinejad, S.: Operator mean inequalities for sector matrices. arXiv:2305.04494

  15. Kubo, F., Ando, T.: Means of positive linear operators. Math. Ann. 246, 205–224 (1980)

    Article  MathSciNet  Google Scholar 

  16. Malekinejad, S., Khosravi, M., Sheikhhosseini, A.: Mean inequalities for sector matrices involving positive linear maps. Positivity 26, 1–17 (2022)

    Article  MathSciNet  Google Scholar 

  17. Matharu, J.S., Aujla, J.S.: Hadamard product version of the Chebyshev and Kantorovich inequalities. J. Inequal. Pure Appl. Math. 10(2), Article 51 (2009)

    MathSciNet  Google Scholar 

  18. Moradi, H.R., Furuichi, S., Sababeh, M.: Operator spectral geometric versus geometric mean. Linear Multilinear Algebra (2023). https://doi.org/10.1080/03081087.2023.2172376

    Article  Google Scholar 

  19. Pečarić, J.E., Furuta, T., Mićić Hot, J., Seo, Y.: Mond–Pečarić Method in Operator Inequalities. Element, Zagreb (2005)

    Google Scholar 

  20. Raissouli, M., Moslehian, M.S., Furuichi, S.: Relative entropy and Tsallis entropy of two accretive operators. C. R. Math. Acad. Sci. Paris. Ser. I 355, 687–693 (2017)

    Article  MathSciNet  Google Scholar 

  21. Sano, T., Sugawara, K.: Operator means for operators with positive definite real part. Adv. Oper. Theory 5, 640–646 (2020)

    Article  MathSciNet  Google Scholar 

  22. Zhang, F.: Matrix Theory. Springer, New York (2011)

    Book  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the referee for his/her valuable comments to improve the paper. Also, the first and third authors would like to thank the Mahani Math Research Institute–Afzallipour Research Institute–Shahid Bahonar University of Kerman.

Author information

Authors and Affiliations

  1. Department of Pure Mathematics Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Alemeh Sheikhhosseini & Maryam Khosravi

  2. Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

    Somayeh Malekinejad

Authors
  1. Alemeh Sheikhhosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Somayeh Malekinejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maryam Khosravi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Somayeh Malekinejad.

Additional information

Communicated by Matjaz Omladic.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheikhhosseini, A., Malekinejad, S. & Khosravi, M. Some Hadamard product inequalities for accretive matrices. Adv. Oper. Theory 9, 12 (2024). https://doi.org/10.1007/s43036-023-00311-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s43036-023-00311-8

Keywords

Mathematics Subject Classification

Search

Navigation