Contractive maps on operator ideals and norm inequalities

Let (I,⦀.⦀)(I,⦀.⦀) be a norm ideal of operators equipped with a unitarily invariant norm ⦀.⦀⦀.⦀. We employ a technique introduced by K.H. Neeb, and used later by H. Kosaki and G. Larotonda to prove that certain ratios of linear operators acting on operators in II are contractive. This leads to new inequalities which are sharper than those proved by F. Kittaneh, and by L. Zou and C. He. We also lift a variety of inequalities to the operator setting which were proved in the matrix setting earlier.