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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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