Abstract
In this paper, several numerical radius inequalities are developed for bounded linear operators defined on a Complex Hilbert space \(\mathcal {H}\) which refine some existing numerical radius inequalities.
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References
Alomari MW (2021) Refinements of some numerical radius inequalities for Hilbert space operators. Linear and Multilinear Algebra 69(7):1208–1223
Abu-Omar A, Kittaneh F (2014) Estimates for the numerical radius and the spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials. Annals Funct Anal 5(1):56–62
Bhunia P, Bag S, Paul K (2019) Numerical radius inequalities and its applications in estimation of zeros of polynomials. Linear Algebra Appl 573:166–177
Bhunia P, Paul K (2021) Proper improvement of well-known numerical radius inequalities and their applications. Results Math 76(4):1–12
Bhunia P, Paul K (2021) New upper bounds for the numerical radius of Hilbert space operators. Bull des Sci Mathématiques 167:102–959
Bhunia P, Jana S, Paul K (2021) Refined inequalities for the numerical radius of Hilbert space operators. arXiv preprint arXiv:2106.13949
Bhunia P, Bag S, Paul K (2021) Bounds for zeros of a polynomial using numerical radius of Hilbert space operators. Annals Funct Anal 12(2):1–14
Buzano ML, della diseguaglianza di Cauchy, G. (1971) Schwarz (Italian), Rend. Sem. Math. Univ. e Politech. Torino 32:405–409
Dragomir SS (2013) Inequalities for the numerical radius of linear operators in Hilbert spaces. Springer, Cham
Dragomir SS (2008) Power inequalities for the numerical radius of a product of two operators in Hilbert spaces. Research report collection, 11(4)
Furuta T (1994) An extension of the Heinz-Kato theorem. Proceedings of the American Mathematical Society, 785-787
Hyder J, Akram MS, Alofi AS, Akter D (2022) On Some numerical radius inequalities involving generalized Aluthge transform. J Funct Spaces 2022:1–9
Heydarbeygi Z, Sababheh M (2022) Moradi HR A convex treatment of numerical radius inequalities. arXiv:2009.07257vI [math.FA]
Gustafson KE, Rao DKM (1997) Num Range. Springer, New York
Kittaneh F, Manasrah Y (2010) Improved Young and Heinz inequalities for matrices. J Math Anal Appl 361(1):262–269
Kittaneh F (2006) Spectral radius inequalities for Hilbert space operators. Proceedings of the American Mathematical Society, 385-390
Kittaneh F (2003) A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix. Studia Math 158(1):11–17
Kittaneh F (2005) Numerical radius inequalities for Hilbert space operators. Studia Math 168(1):73–80
Kittaneh F (2004) Norm inequalities for sums and differences of positive operators. Linear Algebra Appl 383:85–91
Kittaneh F (1988) Notes on some inequalities for Hilbert space operators. Publicat Res Inst Math Sci 24(2):283–293
Pouladi F, Moradi HR (2021) Advanced Refinements of Numerical Radius Inequalities. Int J Math Model Comput, 11(4 (Fall))
Sheikhhosseini A, Moslehian MS, Shebrawi K (2017) Inequalities for generalized Euclidean operator radius via Young’s inequality. J Math Anal Appl 445(2):1516–1529
Yan T, Hyder J, Akram MS, Farid G, Nonlaopon K (2022) On Numerical Radius Bounds Involving Generalized Aluthge Transform. J Funct Spaces 2022:1–8
Zhang Z, Akram MS, Hyder J, Farid G, Yan T (2022) Spectral Radius Formulas Involving Generalized Aluthge Transform. J Funct Spaces 2022:1–8
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Hyder, J., Akram, M.S. On Refinements of Numerical Radius Inequalities. Iran J Sci 47, 915–925 (2023). https://doi.org/10.1007/s40995-023-01438-2
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DOI: https://doi.org/10.1007/s40995-023-01438-2