Preservers of eigenvalue inclusion sets

Aaron Herman, William & Mary
Chi-Kwong Li, William & Mary
Jim Hartman


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.