Let and denote respectively the space of n×n complex matrices and the real space of n×n hermitian matrices. Let p,q,n be positive integers such that p⩽q⩽n. For , the (p,q)-numerical range of A is the set
, where Cp(X) is the pth compound matrix of X, and Jq is the matrix Iq≍On-q. Let denote n or . The problem of determining all linear operators T: → such that