Vol. 52, No. 1, 1974

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Perturbation theory for generalized Fredholm operators

Selwyn Ross Caradus

Vol. 52 (1974), No. 1, 11–15

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 Dieudonné, Saphar, and Crownover.

Mathematical Subject Classification
Primary: 47B30
Received: 15 October 1973
Published: 1 May 1974
Selwyn Ross Caradus