Operator Theory pp 1-5 | Cite as

# Perturbations of Unbounded Fredholm Linear Operators in Banach Spaces

Living reference work entry

First Online:

Received:

Accepted:

## 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

- 1.Gamelin, T.W.: Decomposition theorems for Fredholm operators. Pac. J. Math.
**15**, 97–106 (1965)CrossRefMATHMathSciNetGoogle Scholar - 2.Gohberg, I., Goldberg, S., Kaashoek, M.A.: Classes of Linear Operators. Birkhäuser, Basel (2003)CrossRefMATHGoogle Scholar
- 3.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
- 4.Schechter, M.:, Basic theory of Fredholm operators. Ann. Sc. Norm. Sup. Pisa (3)
**21**, 261–280 (1967)Google Scholar

## Copyright information

© Springer Basel 2014