Skip to main content
Log in

New Norm Equalities and Inequalities for Hankel Operator Matrices

  • Published:
Complex Analysis and Operator Theory Aims and scope Submit manuscript

Abstract

We prove new norm equalities and inequalities for general \(n\times n\) Hankel operator matrices, including pinching type inequalities for weakly unitarily invariant norms.

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.

Institutional subscriptions

Similar content being viewed by others

Data availibility

There is no data availability statement in the manuscript.

References

  1. Audenaert, K.: A norm compression inequality for block partitioned positive semidefinite matrices. Linear Algebra Appl. 413, 155–176 (2006)

    Article  MathSciNet  Google Scholar 

  2. Bani-Domi, W., Kittaneh, F., Shatnawi, M.: New norm equalities and inequalities for certain operator matrices. Math. Inequal. Appl. 23, 1041–1050 (2020)

    MathSciNet  MATH  Google Scholar 

  3. Bhatia, R., Kittaneh, F.: Norm inequalities for partitioned operators and an application. Math. Ann. 287, 719–726 (1990)

    Article  MathSciNet  Google Scholar 

  4. King, C.: Inequalities for trace norms of 2 \({\times }\) 2 block matrices. Commun. Math. Phys. 242, 531–545 (2003)

    Article  MathSciNet  Google Scholar 

  5. King, C., Nathanson, M.: New trace norm inequalities for 2 \({\times }\) 2 blocks of diagonal matrices. Linear Algebra Appl. 389, 77–93 (2004)

    Article  MathSciNet  Google Scholar 

  6. Bhatia, R.: Matrix Analysis. Springer, New York (1997)

    Book  Google Scholar 

  7. Gohberg, I.C., Krein, M.G.: Introduction to the Theory of Linear Nonselfadjoint Operators, Transl. Math. Monographs, 18, American Mathematical Society, Providence, RI, (1969)

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

    MATH  Google Scholar 

  9. Bhatia, R., Kahan, W., Li, R.: Pinchings and norms of block scaled triangular matrices. Linear Multilinear Algebra 50, 15–21 (2002)

    Article  MathSciNet  Google Scholar 

  10. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Products. Seventh Academic Press Inc, San Diego (2007)

    MATH  Google Scholar 

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

    Book  Google Scholar 

  12. 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 

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

    Book  Google Scholar 

  14. Bani-Domi, W., Kittaneh, F.: Norm equalities and inequalities for operator matrices. Linear Algebra Appl. 429, 57–67 (2008)

    Article  MathSciNet  Google Scholar 

  15. Bose, A., Sen, A.: Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices. Electron. Commun. Probab. 12, 21–27 (2007)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fuad Kittaneh.

Additional information

Communicated by Aurelian Gheondea.

Publisher's Note

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

This article is part of the topical collection “Harmonic Analysis and Operator Theory” edited by H. Turgay Kaptanoglu, Aurelian Gheondea and Serap Oztop.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bani-Domi, W., Kittaneh, F. & Shatnawi, M. New Norm Equalities and Inequalities for Hankel Operator Matrices. Complex Anal. Oper. Theory 15, 95 (2021). https://doi.org/10.1007/s11785-021-01136-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11785-021-01136-0

Keywords

Mathematics Subject Classification

Navigation