Norm and numerical radius inequalities for sums of operators in Hilbert spaces

Abstract

By the use of some nonnegative Hermitian forms defined for n-tuple of bounded linear operators on the Hilbert space (H;h·,·i) we establish new numerical radius and operator norm inequalities for sum of products of operators. We obtain among others that…for any n-tuple of operators (T1,...,Tn), (V1,...,Vn). Applications for power series of normal operators with examples are given as well.