Preservers of eigenvalue inclusion sets
Linear Algebra and Its Applications
For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the Brauer region in terms of Cassini ovals, and the Ostrowski region. Characterization is obtained for maps ch on n x n matrices satisfying S(phi(A) - phi(B)) = S(A - B) for all matrices A and B. From these results, one can deduce the structure of additive or (real) linear maps satisfying S(A) = S(phi(A)) for every matrix A. (C) 2010 Elsevier Inc. All rights reserved.
Herman, Aaron; Li, Chi-Kwong; and Hartman, Jim, Preservers of eigenvalue inclusion sets (2010). Linear Algebra and Its Applications, 433(5), 1038-1051.