On the perturbation theory of closed multi-valued linear operators in Banach spaces
by
Sandovici, Adrian
Department of Mathematics, University of Bacau, Str. Spiru Haret, nr. 8, 600114 Bacau, Romania

For a multi-valued linear operator in a linear space the concepts of ascent, descent, nullity, and defect have been introduced and studied. It has been shown that the results of A.E. Taylor and M.A. Kaashoek concerning the relationship between ascent, descent, nullity, and defect for the case of linear operators remain valid in the context of multi-valued linear operators, sometimes under the additional condition that the multi-valued linear operator does not have any nontrivial singular chains.

The purpose of the present talk is to show that the notions of ascent, descent, nullity, and defect can be used in the study of perturbations of multi-valued linear operators in normed spaces, as for example the stability of semi-Fredholm multi-valued linear operators under various perturbations.

Date received: May 4, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawh-38.