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Fredholm Operators

In: Basic Classes of Linear Operators

Author

Listed:
  • Israel Gohberg

    (Tel Aviv University, School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences)

  • Seymour Goldberg

    (University of Maryland, Department of Mathematics)

  • Marinus A. Kaashoek

    (Vrije Universiteit Amsterdam, Department of Mathematics and Computer Science)

Abstract

Fredholm operators are operators that have a finite dimensional kernel and an image of finite codimension. This class includes all operators acting between finite dimensional spaces and operators of the form two-sided invertible plus compact. Fredholm operators appear in a natural way in the theory of Toeplitz operators. The main properties of Fredholm operators, the perturbation theorems and the stability of the index, are presented in this chapter. The proofs are based on the fact that these operators can be represented as finite rank perturbations of one-sided invertible operators.

Suggested Citation

  • Israel Gohberg & Seymour Goldberg & Marinus A. Kaashoek, 2003. "Fredholm Operators," Springer Books, in: Basic Classes of Linear Operators, chapter 0, pages 347-360, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7980-4_15
    DOI: 10.1007/978-3-0348-7980-4_15
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