Numerical radius inequalities and estimation of zeros of polynomials

References

[1] A. Abu-Omar, Spectral radius inequalities for sums of operators with an application to the problem of bounding the zeros of polynomials, Linear Algebra Appl. 550 (2018), 28–36. 10.1016/j.laa.2018.03.033Search in Google Scholar

[2] A. Abu-Omar and F. Kittaneh, Upper and lower bounds for the numerical radius with an application to involution operators, Rocky Mountain J. Math. 45 (2015), no. 4, 1055–1065. 10.1216/RMJ-2015-45-4-1055Search in Google Scholar

[3] P. Bhunia, S. Bag and K. Paul, Bounds for zeros of a polynomial using numerical radius of Hilbert space operators, Ann. Funct. Anal. 12 (2021), no. 2, Paper No. 21. 10.1007/s43034-020-00107-4Search in Google Scholar

[4] P. Bhunia, S. S. Dragomir, M. S. Moslehian and K. Paul, Lectures on Numerical Radius Inequalities, Infosys Sci. Found. Ser., Springer, Cham, 2022. 10.1007/978-3-031-13670-2Search in Google Scholar

[5] P. Bhunia, S. Jana, M. S. Moslehian and K. Paul, Improved inequalities for the numerical radius via Cartesian decomposition, Funct. Anal. Appl. (2023), 10.4213/faa3990. 10.4213/faa3990Search in Google Scholar

[6] P. Bhunia and K. Paul, Furtherance of numerical radius inequalities of Hilbert space operators, Arch. Math. (Basel) 117 (2021), no. 5, 537–546. 10.1007/s00013-021-01641-wSearch in Google Scholar

[7] P. Bhunia and K. Paul, New upper bounds for the numerical radius of Hilbert space operators, Bull. Sci. Math. 167 (2021), Paper No. 102959. 10.1016/j.bulsci.2021.102959Search in Google Scholar

[8] P. Bhunia and K. Paul, Proper improvement of well-known numerical radius inequalities and their applications, Results Math. 76 (2021), no. 4, Paper No. 177. 10.1007/s00025-021-01478-3Search in Google Scholar

[9] P. Bhunia and K. Paul, Annular bounds for the zeros of a polynomial from companion matrices, Adv. Oper. Theory 7 (2022), no. 1, Paper No. 8. 10.1007/s43036-021-00174-xSearch in Google Scholar

[10] M. L. Buzano, Generalizzazione della diseguaglianza di Cauchy–Schwarz, Rend. Semin. Mat. Univ. Politec. Torino 31 (1971/73), 405–409. Search in Google Scholar

[11] M. Fujii and F. Kubo, Operator norms as bounds for roots of algebraic equations, Proc. Japan Acad. 49 (1973), 805–808. 10.3792/pja/1195519149Search in Google Scholar

[12] M. Fujii and F. Kubo, Buzano’s inequality and bounds for roots of algebraic equations, Proc. Amer. Math. Soc. 117 (1993), no. 2, 359–361. 10.1090/S0002-9939-1993-1088441-XSearch in Google Scholar

[13] K. E. Gustafson and D. K. M. Rao, Numerical Range, Universitext, Springer, New York, 1997. 10.1007/978-1-4613-8498-4Search in Google Scholar

[14] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University, Cambridge, 1985. 10.1017/CBO9780511810817Search in Google Scholar

[15] T. Kato, Notes on some inequalities for linear operators, Math. Ann. 125 (1952), 208–212. 10.1007/BF01343117Search in Google Scholar

[16] F. Kittaneh, Notes on some inequalities for Hilbert space operators, Publ. Res. Inst. Math. Sci. 24 (1988), no. 2, 283–293. 10.2977/prims/1195175202Search in Google Scholar

[17] F. Kittaneh, Singular values of companion matrices and bounds on zeros of polynomials, SIAM J. Matrix Anal. Appl. 16 (1995), no. 1, 333–340. 10.1137/S0895479893260139Search in Google Scholar

[18] F. Kittaneh, Norm inequalities for sums of positive operators, J. Operator Theory 48 (2002), no. 1, 95–103. Search in Google Scholar

[19] F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Math. 158 (2003), no. 1, 11–17. 10.4064/sm158-1-2Search in Google Scholar

[20] F. Kittaneh, Bounds for the zeros of polynomials from matrix inequalities, Arch. Math. (Basel) 81 (2003), no. 5, 601–608. 10.1007/s00013-003-0525-6Search in Google Scholar

[21] F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math. 168 (2005), no. 1, 73–80. 10.4064/sm168-1-5Search in Google Scholar

[22] F. Kittaneh, M. Odeh and K. Shebrawi, Bounds for the zeros of polynomials from compression matrix inequalities, Filomat 34 (2020), no. 3, 1035–1051. 10.2298/FIL2003035KSearch in Google Scholar

[23] H. Linden, Bounds for zeros of polynomials using traces and determinants, Seminarberichte Fachb. Math. FeU Hagen 69 (2000), 127–146. Search in Google Scholar

[24] C. A. McCarthy, c p , Israel J. Math. 5 (1967), 249–271. 10.1007/BF02771613Search in Google Scholar

[25] S. Sahoo and N. C. Rout, New upper bounds for the numerical radius of operators on Hilbert spaces, Adv. Oper. Theory 7 (2022), no. 4, Paper No. 50. 10.1007/s43036-022-00216-ySearch in Google Scholar

[26] S. Sahoo, N. C. Rout and M. Sababheh, Some extended numerical radius inequalities, Linear Multilinear Algebra 69 (2021), no. 5, 907–920. 10.1080/03081087.2019.1698510Search in Google Scholar

[27] Y. Seo, Numerical radius inequalities related to the geometric means of negative power, Oper. Matrices 13 (2019), no. 2, 489–493. 10.7153/oam-2019-13-37Search in Google Scholar

[28] A. Sheikhhosseini, M. Khosravi and M. Sababheh, The weighted numerical radius, Ann. Funct. Anal. 13 (2022), no. 1, Paper No. 3. 10.1007/s43034-021-00148-3Search in Google Scholar

[29] M. P. Vasić and D. J. Kečkić, Some inequalities for complex numbers, Math. Balkanica 1 (1971), 282–286. Search in Google Scholar

[30] P. Y. Wu and H.-L. Gau, Numerical Ranges of Hilbert Space Operators, Encyclopedia Math. Appl. 179, Cambridge University, Cambridge, 2021. Search in Google Scholar