Abstract:If T is a bounded linear operator with generalized inverse S, i.e. $TST = T$, we obtain conditions so that $T - U$ has a generalized inverse. When T is a Fredholm operator, the conditions become simply the requirement that $I - US$ (or equivalently $I - SU$) is a Fredholm operator. This result includes the classical perturbation theorems where U is required to have a small norm or to be compact.
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- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 72-76
- MSC: Primary 47A55; Secondary 47B30
- DOI: https://doi.org/10.1090/S0002-9939-1977-0435896-8
- MathSciNet review: 0435896