Numerical Radius Inequalities for Several Operators - Hirzallah, Omar; Kittaneh, Fuad (MATHEMATICA SCANDINAVICA, 2014)
Let A, B, X, and A_1,…,A_2n be bounded linear operators on a complex Hilbert space. It is shown that \[ w(_k=1^2n-1A_k+1^*XA_k+A_1^*XA_2n) ≤ 2( _k=1^nA_2k-1^2)^1/2(_k=1^nA_2k^2)^1/2w(X) \] and \[ w(AB± BA)≤ 22 Bw^2(A)-Re A^2-Im A^22 , \] where w(·) and · are the numerical radius and the usual operator norm, respectively. These inequalities generalize and refine some earlier results of Fong and Holbrook. Some applications of our results are given.