Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 19 (2024), 317 -- 330

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This work is licensed under a Creative Commons Attribution 4.0 International License.

NUMERICAL RADIUS EQUALITIES AND INEQUALITIES FOR HILBERT SPACE OPERATORS

Abdelkader Frakis and Fuad Kittaneh

Abstract. We give new numerical radius equalities and inequalities for Hilbert space operators. Also, we provide some upper bounds for the numerical radii of certain 2 × 2 operator matrices.

2020 Mathematics Subject Classification: 47A08; 47A12; 47A30; 47B15.
Keywords: Normal operator; numerical radius; operator norm; inequality.

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References

  1. A. Abu-Omar, F. Kittaneh, Upper and lower bounds for the numerical radius with an application to involution operators, Rocky Mountain J. Math. 45 (2015), 1055- 1064. MR3418181. Zbl 1339.47007.

  2. A. Abu-Omar, F. Kittaneh, Numerical radius inequalities for n × n operator matrices, Linear Algebra Appl. 468 (2015), 18-26. MR3293237. Zbl 1316.47005.

  3. S. Aici, A. Frakis, F. Kittaneh, Refinements of some numerical radius inequalities for operators, Rend. Circ. Mat. Palermo (2) 72 (2023), 3815–3828. MR4670914. Zbl 07783220.

  4. A. Ammar, A. Frakis, F. Kittaneh, Numerical radius inequalities for the off-diagonal parts of 2× 2 operator matrices, Quaest. Math. 46 (2023), 1-10. MR4650427. Zbl 07755237.

  5. P. Bhunia, S. S. Dragomir, M. S. Moslehian, K. Paul, Lectures on Numerical Radius Inequalities, Infosys Science Foundation Series in Mathematical Sciences, Springer Cham, (2022), XII+209 pp. https://doi.org/10.1007/978- 3-031-13670-2.

  6. S. S. Dragomir, Some inequalities for the Euclidean operator radius of two operators in Hilbert spaces, Linear Algebra Appl. 419 (2006), 256-264. MR2263120. Zbl 1112.47001.

  7. M. El-Haddad, F. Kittaneh, Numerical radius inequalities for Hilbert space operators. II, Studia Math. 182 (2007), 133-140. MR2338481. Zbl 1130.47003.

  8. A. Frakis, F. Kittaneh, S. Soltani, New numerical radius inequalities for operator matrices and a bound for the zeros of polynomials, Adv. Oper. Theory 8 (2023), Paper No. 5, 13 pp. MR4518099. Zbl 07630100.

  9. T. Furuta, Applications of polar decompositions of idempotent and 2-nilpotent operators, Linear Multilinear Algebra 56 (2008), 69-79. MR2378303. Zbl 1129.47022.

  10. G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, Cambridge, 1988.

  11. O. Hirzallah, F. Kittaneh, K. Shebrawi, Numerical radius inequalities for certain 2× 2 operator matrices, Integr. Equ. Oper. Theory 71 (2011), 129–147. MR2822431. Zbl 1238.47004.

  12. C. R. Johnson, F. Zhang, An operator inequality and matrix normality, Linear Algebra Appl. 240 (1996), 105-110. MR1448363. Zbl 0853.47002.

  13. F. Kittaneh, Notes on some inequalities for Hilbert space operators, Publ. Res. Inst. Math. Sci. 24 (1988), 283-293. MR0944864. Zbl 0655.47009.

  14. F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math. 168 (2005), 73-80. MR2133388. Zbl 1072.47004.

  15. F. Kittaneh, Numerical radius inequalities associated with the Cartesian decomposition, Math. Inequal. Appl. 18 (2015), 915-927. MR3344737. Zbl 1334.47007.

  16. K. Paul, S. Bag, On numerical radius of a matrix and estimation of bounds for zeros of a polynomial, Int. J. Math. Sci. (2012) Art. ID 129132, 15 pp. MR2983787. Zbl 1253.65056.

  17. S. Soltani, A. Frakis, Further refinements of some numerical radius inequalities for operators, Oper. Matrices 17 (2023), 245–257. MR4577952. Zbl 07811176.



Abdelkader Frakis
Department of Mathematics,
Mustapha Stambouli University,
Mascara, Algeria.
E-mail: frakis.aek@univ-mascara.dz

Fuad Kittaneh
Department of Mathematics,
The University of Jordan,
Amman, Jordan.
and
Department of Mathematics,
Korea University,
Seoul 02841, South Korea.
E-mail: fkitt@ju.edu.jo



http://www.utgjiu.ro/math/sma