Linear operators that preserve the c -numerical range or radius of matrices
Chi-Kwong Li, Nam‐Kiu Tsing · Linear and Multilinear Algebra · 1988
Let For any n × n matrix A, define the c-numerical range and the c-numerical radius by and rc (A) = max{|z|: z∈ W c (A)} respectively. We give a characterization for those linear operators Twhich satisfy for all matrix A. Moreover, we give a full description for the extreme points of the unit ball in the real linear space of n × n hermitian matrices with respect to the norm rc (·).