Citation: | Mohammad Sababheh, Hamid Reza Moradi. NUMERICAL RADIUS OF KRONECKER PRODUCT OF MATRICES[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2943-2954. doi: 10.11948/20230064 |
In this article, we present several bounds for the numerical radius of the Kronecker product of matrices to enrich our knowledge about this topic.
[1] | E. Alizadeh and A. Farokhinia, Some refinements of numerical radius inequalities for Hilbert space operators, Jordan J. Math. Stat., 2022, 15(1), 55–63. |
[2] | R. Bhatia, Matrix Analysis, Springer-Verlag, New York, 1997. |
[3] | M. L. Buzano, Generalizzazione della diseguaglianza di Cauchy-Schwarz, (Italian) Rend Sem Mat Univ E Politech Torino., 1974, 31 (1971/73), 405–409. |
[4] | S. S. Dragomir, Power inequalities for the numerical radius of a product of two operators in Hilbert spaces, Sarajevo J. Math., 2009, 5(18), 269–278. |
[5] | M. El-Haddad and F. Kittaneh, Numerical radius inequalities for Hilbert space operators. II, Studia Math., 2007, 182(2), 133–140. doi: 10.4064/sm182-2-3 |
[6] | T. Furuta, Invitation to Linear Operators, Taylor and Francis, London, 2001. |
[7] | H. Gau, K. Wang, and P. Wu, Numerical radii for tensor products of operators, Integr. Equ. Oper. Theory, 2014, 78, 375–382. doi: 10.1007/s00020-013-2098-5 |
[8] | D. Gueridi and F. Kittaneh, Inequalities for the Kronecker product of matrices, Ann. Funct. Anal., 2022, 13, 50. https://doi.org/10.1007/s43034-022-00191-8 doi: 10.1007/s43034-022-00191-8 |
[9] | Z. Heydarbeygi, M. Sababheh and H. R. Moradi, A convex treatment of numerical radius inequalities, Czechoslov. Math. J., 2022, 72(147), 601–614. |
[10] | H. Jafarmanesh and M. Khosravi, Sharp operator mean inequalities of the numerical radii, Oper. Matrices, 2021, 15(2), 423–433. |
[11] | Y. Ke, Finite iterative algorithm for the complex generalized Sylvester tensor equations, J. Appl. Anal. Comput., 2020, 10(3), 972–985. |
[12] | F. Kittaneh, Norm inequalities for certain operator sums, J. Funct. Anal., 1997, 103, 337–348. |
[13] | F. Kittaneh, Norm inequalities for sums and differences of positive operators, Linear Algebra Appl., 2004, 383, 85–91. doi: 10.1016/j.laa.2003.11.023 |
[14] | F. Kittaneh, Notes on some inequalities for Hilbert Space operators, Publ. Res. Inst. Math. Sci., 1988, 24(2), 283–93. doi: 10.2977/prims/1195175202 |
[15] | F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math., 2005, 168(1), 73–80. doi: 10.4064/sm168-1-5 |
[16] | F. Kittaneh and H. R. Moradi, Cauchy-Schwarz type inequalities and applications to numerical radius inequalities, Math. Inequal. Appl., 2020, 23(3), 1117–1125. |
[17] | G. Luo, M. Yang, X. Ma, Y. Zhang and S. He, Orthogonal arrays obtained by array subtraction, J. Appl. Anal. Comput., 2021, 11(6), 2815–2839. |
[18] | F. P. Najafabadi and H. R. Moradi, Advanced refinements of numerical radius inequalities, Int. J. Math. Mod. Comp., 2021, 11(4), 1–10. |
[19] | M. E. Omidvar and H. R. Moradi, New estimates for the numerical radius of Hilbert space operators, Linear Multilinear Algebra, 2021, 69(5), 946–956. doi: 10.1080/03081087.2020.1810200 |
[20] | M. E. Omidvar and H. R. Moradi, Better bounds on the numerical radii of Hilbert space operators, Linear Algebra Appl., 2020, 604, 265–277. doi: 10.1016/j.laa.2020.06.021 |
[21] | M. Sababheh, H. R. Moradi and I. Gumus, Some new operator inequalities, Oper. Matrices, 2020, 14(1), 105–115. |
[22] | M. Sattari, M. S. Moslehian and T. Yamazaki, Some generalized numerical radius inequalities for Hilbert space operators, Linear Algebra Appl., 2015, 470, 216–227. doi: 10.1016/j.laa.2014.08.003 |
[23] | A. Sheikhhosseini, M. Khosravi and M. Sababheh, The weighted numerical radius, Ann. Funct. Anal., 2022, 13, 3. https://doi.org/10.1007/s43034-021-00148-3. doi: 10.1007/s43034-021-00148-3 |
[24] | S. Sheybani, M. Sababheh and H. R. Moradi, Weighted inequalities for the numerical radius, Vietnam J. Math., 2023, 51(2), 363–377. doi: 10.1007/s10013-021-00533-4 |
[25] | J. Wang, Y. Zheng and Z. Jiang, Norm qualities and inequalities for tridiagonal perturbed Toeplitz operator matrices, J. Appl. Anal. Comput., 2023, 13(2), 671–683. |
[26] | T. Yamazaki, On upper and lower bounds of the numerical radius and an equality condition, Studia Math., 2007, 178(1), 83–89. doi: 10.4064/sm178-1-5 |
[27] | G. Zhao, H. Li, P. Duan and F. Alsaadi, Survey on applications of semi-tensor product methods in networked evolutionary games, J. Appl. Anal. Comput., 2020, 10(1), 32–54. |