Proyecciones Journal of Mathematics Vol. 31, N^o 3, pp. 277-297, Sepember 2012. Universidad Católica del Norte Antofagasta - Chile

 

New numerical radius inequalities for certain operaor matrices

 

Watheq Bani-Domi

Yarmouk University, Jordan

Feras Ali Bani-Ahmad

Hashemite University, Jordan

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ABSTRACT

In this paper we prove some upper and lower bounds for the numerical radius of the off-diagonal part of 3 X 3 operator matrices and some bounds for the numerical radius inequalities of the general 3 X 3 operator matrix.

Keywords. Numerical radius, Operator norm, Operator matrix, Inequality, Off-diagonal part.

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REFERENCES

[1] Bani-Domi, W., Kittaneh, F.: Norm equalities and inequalities for operator matrices. Linear Algebra and its Applications 429, pp. 57-67, (2008).         [ Links ]

[2] Bani-Domi, W., Kittaneh, F.: Numerical radius inequalities for operator matrices. Linear Multilinear Algebra 57, pp. 421-427, (2009).         [ Links ]

[3] Bhatia, R.: Matrix Analysis. Springer, New York, (1997).         [ Links ]

[4] Halmos, P. R.: A Hilbert Space Problem Book, 2nd ed. Springer, New York, (1982).         [ Links ]

[5] Hirzallah, O., Kittaneh, F., Shebrawi, K.: Numerical radius inequalities for commutators of Hilbert space operators. Numer. Funct. Anal.Optim, pp. 32, pp. 739-749, (2011).

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

 

Watheq Bani-Domi

Department of Mathematics Yarmouk University Irbed, Jordan Watheq@yu.edu.jo

Feras Ali Bani-Ahmad

Department of Mathematics Hashemite University Zarqa, Jordan fbani ahmad@hu.edu.jo

Received : June 2012. Accepted : July 2012