On the numerical radius of an upper triangular operator matrix

Main Article Content

Mehdi Naimi
Mohammed Benharrat
https://orcid.org/0000-0001-5766-6717

Abstract

The main purpose of this paper is to give an improvement of numerical radius inequality for an upper triangular operator matrix.

Article Details

How to Cite
Naimi, M., & Benharrat, M. (2023). On the numerical radius of an upper triangular operator matrix. Tamkang Journal of Mathematics. https://doi.org/10.5556/j.tkjm.55.2024.5094
Section
Papers

References

P. A. Fillmore, J. G. Stampfli, J. P. Williams, On the essential numerical range, the essential spectrum, and a problem of Halmos, Acta Sci. Math. (Szeged), 33 (1972), 179-192.

S. R. Foguel, A counter example to a problem of Sz.-Nagy, Proc. Amer. Math. Soc, 15 (1964), 788–790.

S. R. Garcia, The norm and modulus of a Foguel operator, Indiana Univ. Math. J, 58 (2009), 2305-2315.

H. L. Gau, K. Z. Wang and P. Y. Wu, Numerical ranges of Foguel operators, Linear Algebra Appl., 610 (2021), 766-784.

K. E. Gustafson and D. K. M. Rao, Numerical range. The field of values of linear operators and matrices, Springer-Verlag, New York, 1997.

O. Hirzallah, F. Kittaneh, K. Shebrawi, Numerical Radius Inequalities for Certain $2 times 2$ Operator Matrices. Integr. Equ. Oper. Theory, 71 (2011), 129-147.

F. Kittaneh, A numerical radius inequalities and an estimate for the numerical radius of the Frobenius companion matrix. Studia Math, 158 (2003), 11-17.

F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Mathematica, 168.1 (2005), pp. 73-80.

B. Sz.-Nagy, Completely continuous operators with uniformly bounded iterates, Magyar Tud. Akad. Mat. Kutat'{o} Int. K"{o}zl, 4 (1959), 89-93.