Norm inequalities for the absolute value of Hilbert space operators

Abstract

We use norm inequalities for operators, such as Cauchy–Schwarz inequality and Minkowski inequality, to establish sharp norm inequalities for the absolute value of operators. Among other inequalities, it is shown that if A, B and X are operators on a Hilbert space, such that X is self-adjoint, and r ≥ 1, then This inequality generalizes some earlier related results. Other related inequalities are also discussed.