Perturbation theory for generalized Fredholm operators
Selwyn Caradus · Pacific Journal of Mathematics · 1974
Successful development of the theory of Fredholm and semi-Fredholm operators and a general recognition of the importance of the subject provides an impetus for the study of various generalizations.In this paper, a study is made of operators whose ranges and null spaces are closed complemented subspaces.In particular, if T is such an operator, a rather general sufficient condition is obtained to ensure that T -U is of the same kind.This perturbation theorem includes, as special cases, previous results due to Dieudonne, Saphar, and Crownover.1* Definitions and basic properties* If X is a Banach space, 10.W. T. Reid, Generalized Inverses of Differential and Integral Operators, Proceeding of the Symposium on Theory and Applications of Generalized Inverse of Matrices, Lubbock, Texas, (1968), 1-25.11.P, Saphar, Contribution a Vetude des applications lineaires dans un espace de Banach, Bull.