Bounds for zeros of a polynomial using numerical radius of Hilbert space operators
Tóm tắt
We obtain bounds for the numerical radius of
$$2 \times 2$$
operator matrices which improve on the existing bounds. We also show that the inequalities obtained here generalize the existing ones. As an application of the results obtained here, we estimate the bounds for the zeros of a monic polynomial and illustrate with numerical examples that the bounds are better than the existing ones.
Tài liệu tham khảo
Abu-Omar, A., Kittaneh, F.: Generalized spectral radius and norm inequalities for Hilbert space operators, Internat. J. Math. 26(12) (2015) 1550097 9 pp
Abu-Omar, A., Kittaneh, F.: Estimates for the numerical radius and the spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials. Ann. Funct. Anal. 5(1), 56–62 (2014)
Al-Dolat, M., Al-Zoubi, K., Ali, M., Bani-Ahmad, F.: General numerical radius inequalities for matrices of operators. Open Math. 14, 109–117 (2016)
Alpin, Y.A., Chien, M., Yeh, L.: The numerical radius and bounds for zeros of a polynomial. Proc. Amer. Math. Soc. 131, 725–730 (2002)
Bhunia, P., Bag, S., Paul, K.: Numerical radius inequalities and its applications in estimation of zeros of polynomials. Linear Algebra Appl. 573, 166–177 (2019)
Bag, S., Bhunia, P., Paul, K.: Bounds of numerical radius of bounded linear operator using \(t\)-Aluthge transform. Math. Inequal. Appl. 23(3), 991–1004 (2020)
Bhunia, P., Paul, K., Nayak, R.K.: On inequalities for A-numerical radius of operators. Electron. J. Linear Algebra 36, 143–157 (2020)
Bhatia, R.: Matrix Analysis. Springer, New York (1997)
Fujii, M., Kubo, F.: Buzano’s inequality and bounds for roots of algebraic equations. Proc. Amer. Math. Soc. 117(2), 359–361 (1993)
Hirzallah, O., Kittaneh, F., Shebrawi, K.: Numerical radius inequalities for certain \(2\times 2\) operator matrices. Integral Equ. Oper. Theory 71, 129–147 (2011)
Horn, R.A., Johnson, C.R.: Matrix Anallysis. Cambridge University Press, Cambridge (1985)
Klaja, H., Mashreghi, J., Ransford, T.: On mapping theorems for numerical range. Proc. Am. Math. Soc. 144, 3009–3018 (2016)
Kittaneh, F.: Numerical radius inequalities for Hilbert spaces operators. Stud. Math. 168(1), 73–80 (2005)
Kittaneh, F.: Bounds for the zeros of polynomials from matrix inequalities. Arch. Math. (Basel) 81(5), 601–608 (2003)
Linden, H.: Bounds for zeros of polynomials using traces and determinants. Seminarberichte Fachbereich Mathematik FeU Hagen. 69, 127–146 (2000)
Paul, K., Bag, S.: Estimation of bounds for the zeros of a polynomial using numerical radius. Appl. Math. Comput. 222, 231–243 (2013)
Paul, K., Bag, S.: On the numerical radius of a matrix and estimation of bounds for zeros of a polynomial, Int. J. Math. Math. Sci. 2012 (2012) Article Id 129132 https://doi.org/10.1155/1012/129132.
Shebrawi, K.: Numerical radius inequalities for certain 2\(\times 2\) operator matrices II. Linear Algebra Appl. 523, 1–12 (2017)
Yamazaki, T.: On upper and lower bounds of the numerical radius and an equality condition. Stud. Math. 178(1), 83–89 (2007)