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Perturbations of Unbounded Fredholm Linear Operators in Banach Spaces

  • Toka  Diagana
Living reference work entry

Abstract

In Gohberg et al. (Classes of linear operators, Theorem 4.2, Chapter XVII. Birkhäuser, Basel, 2003), some sufficient conditions are given so that if A is an unbounded Fredholm linear operator and if B is another (possibly unbounded) linear operator, then their algebraic sum A + B is a Fredholm operator. The main objective here consists of extending the previous result to the case of three unbounded linear operators. Namely, some sufficient conditions are given so that if A , B , C are three unbounded linear operators with A being a Fredholm operator, then their algebraic sum \(A + B + C\) is also a Fredholm operator.

Keywords

Banach Space Integral Equation Linear Operator Differential Operator Operator Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    Gamelin, T.W.: Decomposition theorems for Fredholm operators. Pac. J. Math. 15, 97–106 (1965)CrossRefMATHMathSciNetGoogle Scholar
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    Gohberg, I., Goldberg, S., Kaashoek, M.A.: Classes of Linear Operators. Birkhäuser, Basel (2003)CrossRefMATHGoogle Scholar
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    Gohberg, I., Goldberg, S., Kaashoek, M.A.: Classes of Linear Operators Vol. I. Operator Theory: Advances and Applications, vol. 49. Birkhäuser, Basel (1990)Google Scholar
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    Schechter, M.:, Basic theory of Fredholm operators. Ann. Sc. Norm. Sup. Pisa (3) 21, 261–280 (1967)Google Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsHoward University, College of Arts and SciencesWashingtonUSA

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