Geodesic
Numerical radii inequalities for certain operator sums
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1440-1449 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We give several numerical radius inequalities for the product and the sum of operators in Hilbert space. To do this end, we employ some block matrix methods. The advantage of our results is that they extend and refine some well-known inequalities in the literature. algebra.
Keywords: Numerical radius, norm inequality, block matrix. 
@article{SEMR_2024_21_2_a62,
     author = {Ali Zand Vakili and Ali Farokhinia},
     title = {Numerical radii inequalities for certain operator sums},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1440--1449},
     year = {2024},
     volume = {21},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a62/}
}
TY  - JOUR
AU  - Ali Zand Vakili
AU  - Ali Farokhinia
TI  - Numerical radii inequalities for certain operator sums
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 1440
EP  - 1449
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a62/
LA  - en
ID  - SEMR_2024_21_2_a62
ER  - 
%0 Journal Article
%A Ali Zand Vakili
%A Ali Farokhinia
%T Numerical radii inequalities for certain operator sums
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 1440-1449
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a62/
%G en
%F SEMR_2024_21_2_a62
Ali Zand Vakili; Ali Farokhinia. Numerical radii inequalities for certain operator sums. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1440-1449. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a62/

[1] R. Bhatia, Matrix Analysis, Springer, New York, NY, 1996 | Zbl

[2] M. L. Buzano, “Generalizzazione della diseguaglianza di Cauchy–Schwarz'”, Rend. Sem. Mat. Univ. Politech. Torino, 31, 1971-72/1972-73 (1974), 405–409 | Zbl

[3] C. Conde, M. Sababheh, H. R. Moradi, Some weighted numerical radius inequalities, 2022, arXiv: 2204.07620 [math.FA]

[4] S. S. Dragomir, Kato's Type Inequalities for Bounded Linear Operators in Hilbert Spaces, Springer, Cham, 2019 | DOI | Zbl

[5] T. Furuta, Invitation to linear operators. From matrices to bounded linear operators on a Hilbert space, Taylor and Francis, London, 2001 | Zbl

[6] T. Furuta, J. Mićić Hot, J. Pečarić, and Y. Seo, Mond-Pečarić Method in Operator Inequalities. Inequalities for bounded selfadjoint operators on a Hilbert space, Element, Zagreb, 2005 | Zbl

[7] K. E. Gustafson, D. K. M. Rao, Numerical Range: The Field of Values of Linear Operators and Matrices, Springer, New York, NY, 1996 | Zbl

[8] M. Hassani, M. E. Omidvar, H. R. Moradi, “New estimates on numerical radius and operator norm of Hilbert space operators”, Tokyo J. Math., 44:2 (2021), 439–449 | DOI | Zbl

[9] O. Hirzallah, F. Kittaneh, K. Shebrawi, “Numerical radius inequalities for commutators of Hilbert space operators”, Numer. Funct. Anal. Optim., 32:7 (2011), 739–749 | DOI | Zbl

[10] F. Kittaneh, “A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix”, Stud. Math., 158:1 (2003), 11–17 | DOI | Zbl

[11] F. Kittaneh, “Norm inequalities for certain operator sums”, J. Funct. Anal., 143:2 (1997), 337–348 | DOI | Zbl

[12] F. Kittaneh, “Numerical radius inequalities for Hilbert space operators”, Stud. Math., 168:1 (2005), 73–80 | DOI | Zbl

[13] F. Kittaneh, H. R. Moradi, “Cauchy-Schwarz type inequalities and applications to numerical radius inequalities”, Math. Inequal. Appl., 23:3 (2020), 1117–1125 | DOI | Zbl

[14] M. Sababheh, C. Conde, H. R. Moradi, Further numerical radius inequalities, 2022, arXiv: 2204.12045 [math.FA]

[15] M. Sababheh, H. R. Moradi, Z. Heydarbeygi, “Buzano, Kreĭn and Cauchy-Schwarz inequalities”, Oper. Matrices, 16:1 (2022), 239–250 | DOI | Zbl

[16] M. Sattari, M. S. Moslehian, T. Yamazaki, “Some generalized numerical radius inequalities for Hilbert space operators”, Linear Algebra Appl., 470 (2015), 216–227 | DOI | Zbl

[17] S. Sheybani, M. Sababheh, H. R. Moradi, “Weighted inequalities for the numerical radius”, Vietnam J. Math., 51:2 (2023), 363–377 | DOI | Zbl

[18] T. Yamazaki, “On upper and lower bounds of the numerical radius and an equality condition”, Stud. Math., 178:1 (2007), 83–89 | DOI | Zbl