q-numerical radius inequalities for two by two operator matrices
*M. H. M. RashidCorresponding authormalik_okasha@yahoo.commrash@mutah.edu.joDepartment of Mathematics & StatisticsFaculty of ScienceMutah UniversityAlkarak, P. O. Box (7), Jordan0000-0002-3816-5287View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Mar 2024
- Published Online:
- 01 Apr 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2066
- Pages:
- 1–16
Abstract
Keywords
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References
[1] P. Bhunia, S. Bag, and K. Paul, Numerical radius inequalities and its applications in estimation of zeros of polynomials, Linear Algebra Appl., vol.573, pp.166-177 (2019). https://doi.org/10.1016/j.laa.2019.03.017.
[2] H. Bohr, A theorem concerning power series, Proc. Lond. Math. Soc., vol.2, no.13, pp.1-5 (1914).
[3] T. Bottazzi and C. Conde, Generalized Buzano’s Inequality, Filomat, vol.37, no.27, pp.9377-9390 (2023). https://doi.org/10.2298/FIL2327377B.
[4] M.T. Chien and H. Nakazato, Davis-Wielandt shell and q-numerical range, Linear Algebra Appl., vol. 340, pp. 15-31 (2002). https://doi.org/10.1016/S0024-3795(01)00395-0.
[5] M.T. Chien and H. Nakazato, The q-numerical radius of weighted shift operators with periodic weights, Linear Algebra Appl., vol.422, pp.198-218 (2007). https://doi.org/10.1016/j.laa.2006.09.017.
[6] M.T. Chien, The numerical radius of a weighted shift operator, RIMS Kŏkyŭroku, vol.1778, pp.70-77 (2012).
[7] S. S. Dragomir, Some inequalities for the Euclidean operator radius of two operators in Hilbert spaces, Linear Algebra Appl., vol.419, pp.256-264 (2006). https://doi.org/10.1016/j.laa.2006.04.017.
[8] S.S. Dragomir, Inequalities for the norm and numerical radius of composite operator in Hilbert spaces, Internat Ser Numer Math., vol.157,pp.135-146 (2008).
[9] T. Furuta, Norm inequalities equivalent to Lowner-Heinz theorem, Rev Math Phys., vol.1, pp.135-137 (1989).
[10] M. Goldberg and E. Tadmor,On the numerical radius and its applications, Linear Algebra Appl., vol.42, pp.263-284 (1982). https://doi.org/10.1016/0024-3795(82)90155-0.
[11] M. Guesba, On some numerical radius inequalities for normal operators in Hilbert spaces, J. Interdiscip. Math., vol. 25, no. 2, pp. 463-470 (2021). https://doi.org/10.1080/09720502.2021.1930658.
[12] O. Hirzallah, F. Kittaneh, and K. Shebrawi, Numerical radius inequalities for certain 2×2 operator matrices, Integral Equ. Oper. Theory, vol.71, pp.129-147 (2011).
[13] F. Kittaneh, Notes on some inequalities for Hilbert space operators, Publ. Res. Inst. Math. Sci., vol.24, pp. 283-293, 1988.
[14] F. Kittaneh, Norm inequalities for sums of positive operators, J. Operator Theory, vol.48, pp.95-103 (2002).
[15] F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Math., vol.158, no.1, pp.11-17 (2003).
[16] F. Kittaneh, Numerical radius for Hilbert space operators, Studia Math., vol.168, no.1, pp.73-80 (2005).
[17] C. K. Li, P. P. Metha, and L. Rodman, A generalized numerical range: the range of a constrained sesquilinear form, Linear Multilinear Algebra, vol.37, pp.25-50, 1994.
[18] C. K. Li and H. Nakazato, some results on the q-numerical, Linear Multilinear Algebra, vol.43, pp.385-409 (1998).
[19] M. Marcus and P. Andresen, Constrained extrema of bilinear functionals, Monutsh Math., vol.84, pp.219-235 (1977).
[20] S. F. Moghaddam, A. K. Mirmostafaee, and M. Janfada, q-Numerical radius inequalities for Hilbert space, Linear Multilinear Algebra, vol.72, pp.751-763 (2023). DOI: 10.1080/03081087.2022.2161460.
[21] R. Rajic, A generalized q-numerical range, Math Commun., vol.10, pp.31-45 (2005).
[22] N. K. Tsing, The constrained bilinear form and the C-numerical ranges, Linear Algebra Appl., vol.56, pp.195-206 (1984).
[23] A. Zamani and K. Shebrawi, Some upper bounds for the Davis-Wielandt radius of Hilbert space operators, Mediterr. J. Math., vol.17, pp.1-13 (2020).




