Contractive maps on operator ideals and norm inequalities III

Let (I,⦀.⦀) be a norm ideal of operators equipped with a unitarily invariant norm ⦀.⦀. We discuss some generalized Lyapunov type norm inequalities for operators, which are motivated by the work of Bhatia and Drissi [8], Hiai and Kosaki [16] and Jocić [17]. We exploit integral representations and series expansions of certain functions to prove that certain ratios of linear operators acting on operators in I are contractive. This leads to several new and old norm inequalities for operators which were earlier in the matrix settings.