Norm inequalities involving the weighted numerical radii of operators

Abstract

It is shown, among other inequalities, that if A and B are Hilbert space operators which belong to the Schatten p-class, then, for p≥1 and 0<v<1, we have‖A+B‖p≤max⁡(2,2p−1)wp,vp([0AB⁎0])−|1−2v|p‖A−B‖pppandmin⁡(2,2p−1)wp,vp([0AB⁎0])−|1−2v|p|‖A‖p−‖B‖p|pp≤‖A‖p+‖B‖p,where ‖⋅‖p denotes the Schatten p-norm and wp,v is the generalized weighted numerical radius induced by the Schatten p-norm.