Linear Algebra and Its Applications
Denote by M-n the set of n x n complex matrices. Let f : M-n -> [0, infinity) be a continuous map such that f (mu U AU*) = f(A) for any complex unit mu, A is an element of M-n and unitary U is an element of M-n, f(X) = 0 if and only if X = 0 and the induced map t -> f(tX) is monotonically increasing on [0, infinity) for any rank one nilpotent X is an element of M-n. Characterization is given for surjective maps phi on M-n satisfying f (AB - BA) = f (phi(A)phi(B) - phi(B)phi(A)). The general theorem is then used to deduce results on special cases when the function is the pseudo spectrum and the pseudo spectral radius. (C) 2015 Elsevier Inc. All rights reserved.
Cui, J., Li, C. K., & Poon, Y. T. (2016). Preservers of unitary similarity functions on Lie products of matrices. Linear Algebra and its Applications, 498, 160-180.