Numerical radius inequalities for certain 2 × 2 operator matrices II

We give several sharp numerical radius inequalities for certain 2×2 operator matrices. Among other inequalities, it is shown that if A and B be operators in B(H). Thenw([AB00])≤12(‖A‖+‖AA⁎+BB⁎‖12) and2w([0AB0])≤max⁡(‖A‖,‖B‖)+12(‖|A|t|B⁎|1−t‖+‖|B|t|A⁎|1−t‖) for all t∈[0,1], where w(⋅) and ‖⋅‖ denote the numerical radius and the usual operator norm, respectively. The second inequality refines and generalizes earlier inequalities.