Skip to main content
Log in

Further bounds for the Euclidean operator radius of a pair of operators and their applications

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

We give several lower and upper bounds for the Euclidean operator radius of two operators on a Hilbert space. We improve some earlier related bounds. Also, as applications of these bounds, we deduce some new bounds for the classical numerical radius. Some of these bounds are refinements of certain existing bounds.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Data availability

Not applicable.

References

  1. Abu-Omar, A., Kittaneh, F.: Numerical radius inequalities for \(n \times n\) operator matrices. Linear Algebra Appl. 468, 18–26 (2015)

    Article  MathSciNet  Google Scholar 

  2. Aujla, J.S., Silva, F.C.: Weak majorization inequalities and convex functions. Linear Algebra Appl. 369, 217–233 (2003)

    Article  MathSciNet  Google Scholar 

  3. Bhunia, P., Bag, S., Paul, K.: Numerical radius inequalities and its applications in estimation of zeros of polynomials. Linear Algebra Appl. 573, 166–177 (2019)

    Article  MathSciNet  Google Scholar 

  4. Bhunia, P., Dragomir, S.S., Moslehian, M.S., Paul, K.: Lectures on numerical radius inequalities, Infosys Science Foundation Series in Mathematical Sciences. Springer Cham (2022), XII+209 pp. https://doi.org/10.1007/978-3-031-13670-2

  5. Dragomir, S.S.: Some inequalities for the Euclidean operator radius of two operators in Hilbert spaces. Linear Algebra Appl. 419, 256–264 (2006)

    Article  MathSciNet  Google Scholar 

  6. El-Haddad, M., Kittaneh, F.: Numerical radius inequalities for Hilbert space operators. II. Studia Math. 182, 133–140 (2007)

    Article  MathSciNet  Google Scholar 

  7. Halmos, P.R.: A Hilbert Space Problem Book, 2nd edn. Springer, New York (1982)

    Book  Google Scholar 

  8. Hirzallah, O., Kittaneh, F., Shebrawi, K.: Numerical radius inequalities for certain \(2 \times 2\) operator matrices. Integr. Equ. Oper. Theory 71, 129–147 (2011)

    Article  MathSciNet  Google Scholar 

  9. Jana, S., Bhunia, P., Paul, K.: Euclidean operator radius inequalities of a pair of bounded linear operators and their applications. Bull. Braz. Math. Soc. (N.S) 54, 14 (2023)

    MathSciNet  Google Scholar 

  10. Kittaneh, F.: Notes on some inequalities for Hilbert space operators. Publ. Res. Inst. Math. Sci. 24, 283–293 (1988)

    Article  MathSciNet  Google Scholar 

  11. Moradi, H.R., Sababheh, M.: New estimates for the numerical radius. Filomat 35, 4957–4962 (2021)

    Article  MathSciNet  Google Scholar 

  12. Zamani, A., Moslehian, M.S., Xu, Q., Fu, C.: Numerical radius inequalities concerning with algebraic norms. Mediterr. J. Math. 18, 18–38 (2021)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the referees for their useful comments and suggestions.

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to each part of this work equally, and they all read and approved the final manuscript.

Corresponding author

Correspondence to Fuad Kittaneh.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Aici, S., Frakis, A. & Kittaneh, F. Further bounds for the Euclidean operator radius of a pair of operators and their applications. Afr. Mat. 35, 48 (2024). https://doi.org/10.1007/s13370-024-01189-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13370-024-01189-2

Keywords

Mathematics Subject Classification

Navigation