Let H-1, H-2 be two Hilbert spaces, and let T : H-1 --> H-2 be a bounded li
near operator with closed range. We present some representations of the per
turbation for the Moore-Penrose inverse in Hilbert spaces for the case that
the perturbation does not change the range or the null space of the operat
or. (C) 2001 Elsevier Science Ltd. All rights reserved.