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Keywords:
numerical radius; operator norm; mixed Schwarz inequality
numerical radius; operator norm; mixed Schwarz inequality
Summary:
We prove an inner product inequality for Hilbert space operators. This inequality will be utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining new forms that generalize and extend some well known results in the literature, with an application to the newly defined generalized numerical radius. We emphasize that the approach followed in this article is different from the approaches used in the literature to obtain such versions.
References:
[1] Abu-Omar, A., Kittaneh, F.: A generalization of the numerical radius. Linear Algebra Appl. 569 (2019), 323-334. DOI 10.1016/j.laa.2019.01.019 | MR 3907855 | Zbl 07060516
[2] Aujla, J. S., Silva, F. C.: Weak majorization inequalities and convex functions. Linear Algebra Appl. 369 (2003), 217-233. DOI 10.1016/S0024-3795(02)00720-6 | MR 1988488 | Zbl 1031.47007
[3] Baklouti, H., Feki, K., Ahmed, O. A. M. Sid: Joint numerical ranges of operators in semi- Hilbertian spaces. Linear Algebra Appl. 555 (2018), 266-284. DOI 10.1016/j.laa.2018.06.021 | MR 3834203 | Zbl 06914727
[4] Bhunia, P., Bhanja, A., Bag, S., Paul, K.: Bounds for the Davis-Wielandt radius of bounded linear operators. Ann. Funct. Anal. 12 (2021), Article ID 18, 23 pages. DOI 10.1007/s43034-020-00102-9 | MR 4181696 | Zbl 07296618
[5] Bhunia, P., Paul, K., Nayak, R. K.: Sharp inequalities for the numerical radius of Hilbert space operators and operator matrices. Math. Inequal. Appl. 24 (2021), 167-183. DOI 10.7153/mia-2021-24-12 | MR 4221344 | Zbl 07354296
[6] Buzano, M. L.: Generalizzazione della diseguaglianza di Cauchy-Schwarz. Rend. Semin. Mat., Torino Italian 31 (1974), 405-409. MR 0344857 | Zbl 0285.46016
[7] Dragomir, S. S.: Some refinements of Schwartz inequality. Proceedings of the Symposium of Mathematics and Its Applications Timişoara Research Centre of the Romanian Academy, Timişoara (1986), 13-16. Zbl 0594.46018
[8] Dragomir, S. S.: Power inequalities for the numerical radius of a product of two operators in Hilbert spaces. Sarajevo J. Math. 5 (2009), 269-278. MR 2567758 | Zbl 1225.47008
[9] Dragomir, S. S.: Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces. SpringerBriefs in Mathematics. Springer, Cham (2013). DOI 10.1007/978-3-319-01448-7 | MR 3112193 | Zbl 1302.47001
[10] El-Haddad, M., Kittaneh, F.: Numerical radius inequalities for Hilbert space operators. II. Stud. Math. 182 (2007), 133-140. DOI 10.4064/sm182-2-3 | MR 2338481 | Zbl 1130.47003
[11] Halmos, P. R.: A Hilbert Space Problem Book. Graduate Texts in Mathematics 19. Springer, New York (1982). DOI 10.1007/978-1-4684-9330-6 | MR 0675952 | Zbl 0496.47001
[12] Kittaneh, F.: A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix. Stud. Math. 158 (2003), 11-17. DOI 10.4064/sm158-1-2 | MR 2014548 | Zbl 1113.15302
[13] Kittaneh, F.: Norm inequalities for sums and differences of positive operators. Linear Algebra Appl. 383 (2004), 85-91. DOI 10.1016/j.laa.2003.11.023 | MR 2073894 | Zbl 1063.47005
[14] Kittaneh, F.: Numerical radius inequalities for Hilbert space operators. Stud. Math. 168 (2005), 73-80. DOI 10.4064/sm168-1-5 | MR 2133388 | Zbl 1072.47004
[15] Moradi, H. R., Sababheh, M.: More accurate numerical radius inequalities. II. Linear Multilinear Algebra 69 (2021), 921-933. DOI 10.1080/03081087.2019.1703886 | MR 4230456 | Zbl 07333202
[16] Omidvar, M. E., Moradi, H. R., Shebrawi, K.: Sharpening some classical numerical radius inequalities. Oper. Matrices 12 (2018), 407-416. DOI 10.7153/oam-2018-12-26 | MR 3812182 | Zbl 06905101
[17] Pečarić, J., Furuta, T., Hot, J. Mićić, Seo, Y.: Mond-Pečarić Method in Operator Inequalities: Inequalities for Bounded Selfadjoint Operators on a Hilbert Space. Monographs in Inequalities 1. Element, Zagreb (2005). MR 3026316 | Zbl 1135.47012
[18] Sababheh, M.: Numerical radius inequalities via convexity. Linear Algebra Appl. 549 (2018), 67-78. DOI 10.1016/j.laa.2018.03.025 | MR 3784336 | Zbl 06866366
[19] Sababheh, M.: Heinz-type numerical radii inequalities. Linear Multilinear Algebra 67 (2019), 953-964. DOI 10.1080/03081087.2018.1440518 | MR 3923038 | Zbl 07048433
[20] Sababheh, M., Moradi, H. R.: More accurate numerical radius inequalities. I. Linear Multilinear Algebra 69 (2021), 1964-1973. DOI 10.1080/03081087.2019.1651815 | MR 4279169 | Zbl 07394476
[21] Zamani, A.: $A$-numerical radius inequalities for semi-Hilbertian space operators. Linear Algebra Appl. 578 (2019), 159-183. DOI 10.1016/j.laa.2019.05.012 | MR 3953041 | Zbl 07099557
[22] Zamani, A., Moslehian, M. S., Xu, Q., Fu, C.: Numerical radius inequalities concerning with algebra norms. Mediterr. J. Math. 18 (2021), Article ID 38, 13 pages. DOI 10.1007/s00009-020-01665-6 | MR 4203694 | Zbl 07302838
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