Volume 25 , Issue 3 , PP: 307-311, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Mona Sakkijha 1 , Shatha Hasan 2 *
Doi: https://doi.org/10.54216/IJNS.250327
In this paper, we prove new spectral radius inequalities for sums, differences and commutators involving accretive-dissipative matrices of Hilbert space. Earlier well-known results used the spectral radius for its importance for general matrices. In our paper, we focus on some results related to spectral radius for special kind of matrices which are accretive-dissipative. A particular example is also presented in this work.
Spectral radius , Commutators , Accretive-Dissipative Matrices
[1] A. Abu-Omar and F. Kittaneh (2015),Notes on some spectral radius inequalities,Studia Math, 2875, 97- 109.
[2] R. Bhatia and F. Kittaneh (2009), The singular values of A + B and A + iB, Linear Algebra its Applications, 431,1502-1508.
[3] P.R. Halmos, A Hilbert Space Problem Book, 2nd edition, Springer-Verlag, New York, 1982.
[4] J. C. Hou and H.K.Do (1995), Norm inequalities for positive Operator Matrices, Integral Equations Operator Theory,22, 281-294.
[5] F. Kittaneh (2004), Normal inequalities for sums and differences of positive operators, Linear Algebra its Applications,383,85-91.
[6] F. Kittaneh (2005), Spectral Radius Inequalities for Hilbert Space operators, American Mathematical Society, 134,385-390.
[7] F. Kittaneh (2007), Inequalities for commutators of positive operators, Journal of Functional Analysis, 250, 132-143.
[8] F. Kittaneh and M. Sakkijha (2019), Inequalities for accretive-dissipative matrices, Linear and Multilinear Algebra, 67, 1037-1042.
[9] M. Sakkijha and S. Hasan (2024), Hadamard Determinant Inequalities for Accretive-Dissipative Matrices, International Journal of Mathematics and Computer Science, 19,111-116.