Further Seminorm and Numerical Radius Inequalities for Products and Sums of Operators

Our aim in this article is to establish several new norm and numerical radius inequalities for products and sums of operators acting on a complex Hilbert space (H, <center dot, center dot >). Some of the obtained inequalities improve well known ones. In addition, by using new techniques, we prove certain new inequalities related to (omega)A(center dot) and parallel to center dot parallel to A, where (omega)A(T) and parallel to T parallel to (A) denote the A-numerical radius and the A-operator seminormof an operator T acting on the semi-Hilbert space (H, <center dot, center dot > A), respectively. Here < x, y > A := < Ax, y > for every x, y epsilon H.