Refinements of some numerical radius inequalities for Hilbert space operators

Article Sidebar

PDF
Published: May 1, 2023
DOI: https://doi.org/10.5556/j.tkjm.54.2023.4061
Keywords:
numerical radius convex function operator Mixed Schwarz inequality Furuta inequality Young inequality

Main Article Content

Mohammad M.H Rashid
University

Abstract

Some power inequalities for the numerical radius based on the recent Dragomir extension of Furuta's inequality are established. Some particular cases are also provided. Moreover, we get an improvement of the H\"older-McCarthy operator inequality in the case when $r\geq 1$ and refine generalized inequalities involving powers of the numerical radius for sums and products of Hilbert space operators.

Article Details

How to Cite
Rashid, M. M. (2023). Refinements of some numerical radius inequalities for Hilbert space operators. Tamkang Journal of Mathematics, 54(2), 155–173. https://doi.org/10.5556/j.tkjm.54.2023.4061
Issue
Vol. 54 No. 2 (2023)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Author Biography

Mohammad M.H Rashid, University

Mathematics/Prof.Dr

References

S. S. Dragomir, Reverse inequalities for the numerical radius of linear operators in Hilbert spaces, Bull. Austral. Math. Soc., 73 (2) (2006), 255–262.

S. S. Dragomir, Some inequalities for the norm and the numerical radius of linear operators in Hilbert Spaces, Tamkang J. Math., 39 (1) (2008), 1–7.

S. S. Dragomir, Some inequalities generalizing Kato’s and Furuta’s results, Filomat, 28 (1)(2014), 179–195.

T. Furuta, An extension of the Heinz-Kato theorem. Proc. Amer. Math. Soc., 120 (3) (1994), 785–787.

Z. Heydarbeygi and M. Amyari, Some refinements of the numerical radius inequalities via young inequality, Krag. J. Math., 45 (2) (2021), 191–202.

T. Kato, Notes on some inequalities for linear operators, Math. Ann., 125(1952), 208–212.

M. Kian, Operator Jensen inequality for superquadratic functions, Linear Algebra Appl., 456 (2014), 82–87.

F. Kittaneh, Notes on some inequalities for Hilbert Space operators, Publ Res. Inst. Math. Sci., 24 (2) (1988), 283–293.

F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Math.,158 (1) (2003), 11–17.

F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math., 168 (1) (2005), 73–80.

F. Kittaneh and M. El-Haddad, Numerical radius inequalities for Hilbert space operators II, Studia Math., 182 (2) (2007), 133–140.

F. Kittaneh and Y. Manasrah, Improved Young and Heinz inequalities for matrices, J. Math. Anal. Appl., 361 (2010), 262–269.

Y. Al-Manasrah and F. Kittaneh, A generalization of two refined Young inequalities, Positivity, 19 (2015), 757–768.

H. Kober, On the arithmetic and geometric means and on H¨older’s inequality, Proc. Amer. Math. Soc., 9 (1958), 452–459.

H.R. Moradi, S. Furuichi, F.C. Mitroi and R. Naseri, An extension of Jensen’s operator inequality and its application to Young inequality, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat., 113 (2) (2019), 605–614.

J.Pemcari´sc, T. Furuta, J. Mi´sci´sc Hot, and Y. Seo, Mondpencari´ec method in operator inequalities, Inequalities for Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, 2005.

M.H.M.Rashid, Power inequalities for the numerical radius of operators in Hilbert spaces, Khayyam J. Math., 5 2 (2019), 15–29.

K. Shebrawi and H. Albadwi, Numerical radius and operator norm inequalities, J. Inequal. Appl. (2009), Article ID 492154, 11 pages.