Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals

Abstract

If A, B ∈ B(H) are normal contractions, then for every X ∈ which generalizes a result of D.R. Jocić [Proc. Amer. Math. Soc. 126 (1998), no. 9, 2705-2713] for α not being an integer. Similar inequalities in the Schatten p-norms, for non-normal A, B and in the Q-norms if one of A or B is normal, are also given.