Norm Inequalities for Self-Adjoint Derivations

AbstractFor bounded Hilbert space operators and for all unitarily invariant norms there hold||||A−B|p|||⩽2p−1|||A|A|p−1−B|B|p−1|||,for all realp⩾2, and ifAandBare additionally self-adjoint, then||||AX+XB|p|||⩽2p−1‖X‖p−1||||A|p−1AX+XB|B|p−1|||,for all realp⩾3