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Perturbation theory for generalized Fredholm operators. II


Author: S. R. Caradus
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
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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 [Enhancements On Off] (What's this?)

  • [1] F. V. Atkinson, On relatively regular operators, Acta Sci. Math. Szeged 15 (1953), 38–56. MR 0056835
  • [2] S. R. Caradus, Perturbation theory for generalized Fredholm operators, Pacific J. Math. 52 (1974), 11–15. MR 0353034
  • [3] -, Operator theory of the pseudo-inverse, Queen's Papers in Pure and Appl. Math., no. 38, Queen's University, Kingston, Ontario.
  • [4] S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood, Calkin algebras and algebras of operators on Banach spaces, Marcel Dekker, Inc., New York, 1974. Lecture Notes in Pure and Applied Mathematics, Vol. 9. MR 0415345
  • [5] H. Heuser, Funktional Analysis, Stuttgart, 1975.

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DOI: https://doi.org/10.1090/S0002-9939-1977-0435896-8
Article copyright: © Copyright 1977 American Mathematical Society

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