Perturbation theory for generalized Fredholm operators. II
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- by S. R. Caradus PDF
- Proc. Amer. Math. Soc. 62 (1977), 72-76 Request permission
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.References
- F. V. Atkinson, On relatively regular operators, Acta Sci. Math. (Szeged) 15 (1953), 38–56. MR 56835
- S. R. Caradus, Perturbation theory for generalized Fredholm operators, Pacific J. Math. 52 (1974), 11–15. MR 353034 —, Operator theory of the pseudo-inverse, Queen’s Papers in Pure and Appl. Math., no. 38, Queen’s University, Kingston, Ontario.
- S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Applied Mathematics, Vol. 9, Marcel Dekker, Inc., New York, 1974. MR 0415345 H. Heuser, Funktional Analysis, Stuttgart, 1975.
Additional Information
- © 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