Norm inequalities involving the weighted numerical radii of operators

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 parallel to A +B parallel to(p) <= p root mas (2, 2(p-1)) w(p,v)(p) ( [GRAPHICS] ) - vertical bar 1 = 2v vertical bar(p) parallel to A - B parallel to(p)(p) and <= p root min (2, 2(p-1)) w(p,v)(p) ( [GRAPHICS] ) - vertical bar 1 = 2v vertical bar(p) parallel to A parallel to(p) - parallel to B parallel to(p)vertical bar(p) <= parallel to A parallel to(p) + parallel to B parallel to(p), where parallel to center dot parallel to(p) denotes the Schatten p-norm and wp,vis the generalized weighted numerical radius induced by the Schatten p-norm. (c) 2022 Elsevier Inc. All rights reserved.