Norm inequalities for self-adjoint derivations

Abstract

For bounded Hilbert space operators and for all unitarily invariant norms there hold||||A-B| p |||≤2 p-1 |||A|A| p-1 -B|B| p-1 |||,for all realp≥2, and ifAandBare additionally self-adjoint, then||||AX+XB| p |||≤2 p-1 ||X|| p-1 ||||A| p- 1 AX+XB|B| p-1 |||,for all realp≥3. © 1997 Academic Press.