Redirecting to http://dergipark.org.tr/_fragment?_hash=qg9mqCLkFu8hS5St6kJrxTKdhcmqmFvw5q-qJNmHKs8&_path=id%3D1334983%26_format%3Dhtml%26_locale%3Den%26_controller%3DApp%255CController%255CSite%255CArticleController%253A%253AesiArticleStats.
Conference Paper
BibTex RIS Cite

Year 2023, Volume: 22, 15 - 25, 01.09.2023

Mohammed Al-dolat

https://doi.org/10.55549/epstem.1334983

Abstract

References

  • Abu-Omar, A. & Kittaneh, F. (2015). Upper and lower bounds for the numerical radius with an application to involution operators, Rocky Mountain Journal Math., 45(4), 1055-1065.
  • Al-Dolat, M., & Al-Zoubi, K. (2023). Improved and refined numerical radius inequalities for Hilbert space operators.https://assets.researchsquare.com/files/rs2668438/v1/a5b67b067e6f6fddcf09cb22.pdf?c=1678771282
  • Al-Dolat, M., Al-Zoubi, K., Ali, M., & Bani-Ahamed, F. (2016). General numerical radius inequalities for matrices of operators, Open Math., 4, 1-9.
  • Al-Dolat, M., & Jaradat, I. (2023). A refinement of the Cauchy-Shwarz inequality accompanied by new numerical radius upper bounds. Filomat, 37, 971-977.
  • Al-Dolat, M., & Kittaneh, F. (2023). Upper bounds for the numerical radii of powers of Hilbert space operators. Quaestiones Mathematicae, 1-12.
  • Aujla, J., & Silva, F. (2003). Weak majorization inequalities and convex functions. Linear Algebra Appl., 369, 217-233.
  • Bani-Domi W., & Kittaneh, F. (2021). Refined and generalized numerical radius inequalities for 2x2 operator matrices. Linear Algebra Appl. 364-380.
  • Bani-Domi, W. & Kittaneh F. (2021). Norm and numerical radius inequalities for Hilbert space operators. Linear Multilinear Algebra, 69, 934-945.
  • Buzano, M.L. (1974). Generalizzazione della diseguaglianza di Cauchy-Schwarz, (Italian). Rend Sem Mat Univ e Politech Torino, 31, 405-409.
  • Dragomir, S.S. (2009). Power inequalities for the numerical radius of a product of two operators in Hilbert spaces. Sarajevo J Math., 18, 269-278.
  • El-Haddad, M., & Kittaneh, F. (2007). Numerical radius inequalities for Hilbert space operators. II Studia Math., 182, 133-140.
  • Kittaneh, F. & Moradi, H. R. (2020). Cauchy-Schwarz type inequalities and applications to numerical radius inequalities. Mathematical Inequalities and Applications, 23, 1117-1125.
  • Kittaneh, F. (1988). Notes on some inequalities for Hilbert space operators. Pub1. Reserach Inst. Math. Science, 24, 283-293.
  • Kittaneh, F. (2003). A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix. Studia Math., 158, 11-17.
  • Kittaneh, F. (2005) Numerical radius inequalities for Hilbert space operators. Studia Math., 168, 73-80.
  • Moradi, H. ,& Sababheh, M. (2021). New estimates for the numerical radius. Filomat, 35, 4957-4962.
  • Halmos, P.R. (1982). A Hilbert space Problem Book, (2nd ed).New York, NY:Springer.

General Upper Bounds for the Numerical Radii of Powers of Hilbert Space Operators

Year 2023, Volume: 22, 15 - 25, 01.09.2023

Mohammed Al-dolat

https://doi.org/10.55549/epstem.1334983

Abstract

In this paper, we will present several upper bounds for the numerical radii of a operator matrices. We use these bounds to generalize and improve some well-known numerical radius inequalities. We provide a refinement of an earlier numerical radius inequality due to (Bani-Domi & Kittaneh, 2021) [Norm and numerical radius inequalities for Hilbert space operators], (Bani-Domi & Kittaneh, 2021) [Refined and generalized numerical radius inequalities for operator matrices] and (Al-Dolat & Kittaneh, 2023) [Upper bounds for the numerical radii of powers of Hilbert space operators].

Keywords

Numerical radius Usual operator norm Operator matrix Buzano inequality.

References

  • Abu-Omar, A. & Kittaneh, F. (2015). Upper and lower bounds for the numerical radius with an application to involution operators, Rocky Mountain Journal Math., 45(4), 1055-1065.
  • Al-Dolat, M., & Al-Zoubi, K. (2023). Improved and refined numerical radius inequalities for Hilbert space operators.https://assets.researchsquare.com/files/rs2668438/v1/a5b67b067e6f6fddcf09cb22.pdf?c=1678771282
  • Al-Dolat, M., Al-Zoubi, K., Ali, M., & Bani-Ahamed, F. (2016). General numerical radius inequalities for matrices of operators, Open Math., 4, 1-9.
  • Al-Dolat, M., & Jaradat, I. (2023). A refinement of the Cauchy-Shwarz inequality accompanied by new numerical radius upper bounds. Filomat, 37, 971-977.
  • Al-Dolat, M., & Kittaneh, F. (2023). Upper bounds for the numerical radii of powers of Hilbert space operators. Quaestiones Mathematicae, 1-12.
  • Aujla, J., & Silva, F. (2003). Weak majorization inequalities and convex functions. Linear Algebra Appl., 369, 217-233.
  • Bani-Domi W., & Kittaneh, F. (2021). Refined and generalized numerical radius inequalities for 2x2 operator matrices. Linear Algebra Appl. 364-380.
  • Bani-Domi, W. & Kittaneh F. (2021). Norm and numerical radius inequalities for Hilbert space operators. Linear Multilinear Algebra, 69, 934-945.
  • Buzano, M.L. (1974). Generalizzazione della diseguaglianza di Cauchy-Schwarz, (Italian). Rend Sem Mat Univ e Politech Torino, 31, 405-409.
  • Dragomir, S.S. (2009). Power inequalities for the numerical radius of a product of two operators in Hilbert spaces. Sarajevo J Math., 18, 269-278.
  • El-Haddad, M., & Kittaneh, F. (2007). Numerical radius inequalities for Hilbert space operators. II Studia Math., 182, 133-140.
  • Kittaneh, F. & Moradi, H. R. (2020). Cauchy-Schwarz type inequalities and applications to numerical radius inequalities. Mathematical Inequalities and Applications, 23, 1117-1125.
  • Kittaneh, F. (1988). Notes on some inequalities for Hilbert space operators. Pub1. Reserach Inst. Math. Science, 24, 283-293.
  • Kittaneh, F. (2003). A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix. Studia Math., 158, 11-17.
  • Kittaneh, F. (2005) Numerical radius inequalities for Hilbert space operators. Studia Math., 168, 73-80.
  • Moradi, H. ,& Sababheh, M. (2021). New estimates for the numerical radius. Filomat, 35, 4957-4962.
  • Halmos, P.R. (1982). A Hilbert space Problem Book, (2nd ed).New York, NY:Springer.
There are 17 citations in total.

Details

Primary Language English
Subjects Software Engineering (Other)
Journal Section Articles
Authors

Mohammed Al-dolat

Early Pub Date July 30, 2023
Publication Date September 1, 2023
Published in Issue Year 2023 Volume: 22

Cite

APA Al-dolat, M. (2023). General Upper Bounds for the Numerical Radii of Powers of Hilbert Space Operators. The Eurasia Proceedings of Science Technology Engineering and Mathematics, 22, 15-25. https://doi.org/10.55549/epstem.1334983
Creative Commons License