The effect of finite rank perturbations on Jordan chains of linear operators

A general result on the structure and dimension of the root subspaces of a linear operator under finite rank perturbations is proved: The increase of dimension from the n-th power of the kernel of the perturbed operator to the (n + 1)-th power differs from the increase of dimension of the corresponding powers of the kernels of the unperturbed operator by at most the rank of the perturbation. This bound is sharp.Fil: Behrndt, Jussi. Technische Universität Graz. Institut für Numerische Mathematik.; AlemaniaFil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaFil: Leben,Leslie. Technische Universität Graz. Institut für Numerische Mathematik; AlemaniaFil: Trunk, Carsten. Technische Universität Graz. Institut für Numerische Mathematik; Alemani