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,〈·,·〉). Some of the obtained inequalities improve well known ones. In addition, by using new techniques, we prove certain new inequalities related to ωA(·) and ||·||A, where ωA(T) and ||T||A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space (H,〈·,·〉A), respectively. Here 〈x,y〉A:=〈Ax,y〉 for every x,y∈H.