Linear Operators Preserving Decomposable Numerical Radii on Orthonormal Tensors

Let 1 less than or equal to m less than or equal to n, and let chi: H -->C be a degree 1 character on a subgroup H of the symmetric group of degree m. The generalized matrix function on an m x m matrix B = (b(ij)) associated with chi is defined by d(chi)(B) = Sigma (sigma epsilonH)chi(sigma) Pi (m)(rf=1) b(j,sigma (f)), and the decomposable numerical radius of an n x n matrix A on orthonormal tensors associated with chi is defined by r(chi)(perpendicular to)(A) = max{\d(chi)(X*AX)\: X is an n x m matrix such that X*X = I-m}. We study those linear operators L on n x n complex matrices that satisfy rx(L(A)) r(chi)(perpendicular to)(A) for all A is an element of M-n. In particular, it is shown that if 1 less than or equal to m < n, such an operator must be of the form A (bar right arrow) U*AU or A (bar right arrow) xiU*A/U for some unitary matrix U and some xi is an element of C with \ xi \ = 1.