Linear operators preserving decomposable numerical radii on orthonormal tensors

Abstract

Let 1⩽m⩾n, and let χ: 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×m matrix B=(bij ) associated with χ is defined by , and tne decomposable numerical radius of an n×n matrix A on orthonormal tensors associated with χ is defined by . We study those linear operators L on n×n complex matrices that satisfy for all AεMn . In particular, it is shown that if 1⩽m>n, such an operator must be of the form for some unitary matrix U and some .