Linear preservers of higher rank numerical ranges and radii
Sean Clark, Chi-Kwong Li, Jennifer Mahle, Leiba Rodman · Linear and Multilinear Algebra · 2009
Structural theorems regarding linear preservers of the higher rank numerical ranges are proved for the real linear space of bounded self-adjoint operators or the complex linear space of bounded linear operators acting on a Hilbert space. It is shown that the linear preservers of rank k-numerical ranges must be of the standard form: unitary similarity or unitary similarity followed by transposition with respect to a fixed orthonormal basis. Furthermore, it is shown that a linear preserver of the rank k-numerical radius must be a unimodular scalar multiple of a linear preserver of the rank k-numerical range.