Low rank perturbations of strongly definitizable transformations and matrix polynomials (Q1319978)

The authors consider problems concerning the number of real eigenvalues of a \(G\)-selfadjoint transformation \(A\) where \(A\) and \(G\) are low rank perturbations of \(A_ 0\) and \(G_ 0\) and \(A_ 0\) is a \(G_ 0\)- strongly definitizable selfadjoint transformation. Some applications to quadratic matrix polynomials are made.