REFINEMENT OF SOME INEQUALITIES FOR OPERATORS

Year 2015, Volume: 3 Issue: 1, 56 - 62, 01.04.2015

Alemeh Sheıkh Hosseını

Abstract

In this paper, we will use a refinement of the classical Young inequality to improve some inequalities of operators.

Keywords

Inequalities, Numerical radius, Unitarily invariant norms, Young inequality

References

• [1] T. Ando, Matrix Young inequalities, Oper. Theory Adv. Appl., 75, (1995), 33-38.
• [2] R. Bhatia, Positive Denite Matrices , Princeton University Press, 2007.
• [3] R. Bhatia and F. Kittaneh, On the singular values of a product of operators, SIAM J. Matrix Anal. Appl., 11, (1990), 272-277.
• [4] M. El-Haddad and F. Kittaneh, Numerical radius inequalities for Hilbert space operators. II, Studia Mathematica, 182, 2 (2007), 133-140.
• [5] K.E. Gustafson and D.K.M. Rao, Numerical Range, Springer-Verlag, New York, 1997.
• [6] F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Mathematica, 158, 1(2003), 11-17.
• [7] F. Kittaneh, Notes on some inequalities for Hilbert space operators, Publications of the Research Institute for Mathematical Sciences, 24, 2 (1988), 283-293.
• [8] F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Mathematica, 168, (2005) , 73-80.
• [9] F. Kittaneh and Yousef Manasrah, I mproved Young and Heinz inequalities for matrices, J. Math. Anal. Appl. 361, (2010), 262-269.
• [10] A. Salemi and A. Sheikhhosseini, Matrix Young numerical radius inequalities, J. Math. In- equal., 16, (2013), 783-791.
• [11] A. Salemi and A. Sheikhhosseini, On reversing of the modied Young inequality, Ann. Funct. Anal., 5, (2014), 69-75.
• [12] Kh. Shebrawi and H. Albadawi, Numerical radius and operator norm inequalities, J. Inequal. Appl. 2009, (2009), 1-11.