On the numerical radius parallelism of operators for a sesquilinear form

Guesba, Messaoud

doi:10.47974/JIM-1726

Open Access Research Article

On the numerical radius parallelism of operators for a sesquilinear form

^*Messaoud GuesbaCorresponding authorguesba-messaoud@univ-eloued.dzDepartment of MathematicsFaculty of Exact SciencesEchahid Hamma Lakhdar UniversityEl Oued, 39000, AlgeriaView full profile →

* Corresponding author · click or hover a name for details

pp. 77–85Vol. 27Issue 1February 2024DOI: 10.47974/JIM-1726XML

Received:: 09 Nov 2022
Published Online:: 27 Feb 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1726
Pages:: 77–85

Abstract

Our present work introduces a novel notion of numerical radius parallelism for two lineair operators which is related to sesquilinear form. We generalize the well-known results due to Mehrazin et al. in [Bull. Iran. Math. Soc. 46, pages 821-829 (2020)].

Keywords

Sesquilinear form Parallelism Numerical radius Operator

Subject Classifications

(2010) 47A5847A6447B38

References

[1] P. J. Cameron, J. J. Seedel, Quadratic forms over GF(2). Indag. Math., 35, 1-8 (1973).
[2] M. Guesba, M.C. Kaadoud and A. Baghdad, A note on the maximal numerical range of operators for a sesquilinear form, Journal of Interdisciplinary Mathematics, 25(4), 1117-1126 (2022).
[3] M. Guesba, On some numerical radius inequalities for normal operators in Hilbert spaces, Journal of Interdisciplinary Mathematics, 25:2, 463-470 (2022), DOI: 10.1080/09720502.2021.1930658.
[4] M. Marvin, P. Andresen, Constrained extrema of bilinear functionals, Monatsh. Math., 84(3), 219-235 (1977).
[5] M. Mehrazin, M. Amyari, A. Zamani, Numerical Radius Parallelism of Hilbert Space Operators, Bull. Iran. Math. Soc, 46, 821-829 (2020), https://doi.org/10.1007/s41980-019-00295-3.
[6] C. K. Li, P. P. Mehta, L. Rodman, A generalized numerical range: the range of a constrained sesquilinear form, Linear Multilinear Algebra., 37(1-3), 25-49 (1994).
[7] H. R. Moradi, M. E. Omidvar, S. S. Dragomir, M. S. Khan, Sesquilinear version of numerical range and numerical radius. Acta Univ. Sapientiae, Mathematica, 9, 2, 324-335 (2017).
[8] M.S. Moslehian, An operator extension of the parallelogram law and related norm inequalities, Math. Inequal. Appl. 73, 3821-3831 (2010).
[9] J. G. Murphy, Operator theory and C* -algebras, Academic Press, San Diego (1990).
[10] A. Seddik, Rank one operators and norm of elementary operators. Linear Algebra Appl. 424, 177-183 (2007).
[11] A. Zamani, M. S. Moslehian, Exact and approximate operator parallelism, Canad Math Bull. 58(1) : 207-224 (2015).
[12] A. Zamani and M. S. Moslehian, Norm-parallelism in the geometry of Hilbert C*-modules, Indag. Math. (N.S.) 27, No. 1, 266-281 (2016).

Views: 157Downloads: 74Citations: 0