Extremality of numerical radii of matrix commutators and Jordan products

It is known that the numerical radius of the commutator (resp., Jordan product) AB−BA (resp., AB+BA) of two n-by-n matrices A and B is related to those of A and B by w(AB±BA)≤4w(A)w(B). In this paper, we give complete characterizations of A and B for which the equality is attained. The matrices involved can be considered as elaborate generalizations of the equality-attaining A=[0a00] and B=[00b0].