Numerical radius inequalities via block matrices

In this paper, we prove new numerical radius bounds that generalize some well-known results in the literature. For example, we prove that if A, B, X, Y are bounded linear operators on a complex separable Hilbert space H such that A and B are positive, then w(AX + YB) <= root|| A + B || || X (& lowast;) AX + YBY & lowast; ||. This inequality generalizes a celebrated inequality proved by Kittaneh which states that: w(2)(A) <= 1/2|| A(& lowast;)A+AA(& lowast;) ||.