# semi-Fredholm operator

A semi-Fredholm operator is a bounded operator^{} between Banach spaces^{} that has a finite dimensional kernel or cokernel, and closed range.
There are two semigroups of semi-Fredholm operators:
upper semi-Fredholm operators (those which have finite dimensional kernels),
and lower semi-Fredholm operators (those which have finite dimensional cokernels).
A semi-Fredholm operator that is both upper and lower is Fredholm.
If an operator is homotopic through (a norm continuous path of) semi-Fredholm operators to a Fredholm operator, then it is Fredholm.

Title | semi-Fredholm operator |
---|---|

Canonical name | SemiFredholmOperator |

Date of creation | 2013-03-22 14:17:00 |

Last modified on | 2013-03-22 14:17:00 |

Owner | mhale (572) |

Last modified by | mhale (572) |

Numerical id | 5 |

Author | mhale (572) |

Entry type | Definition |

Classification | msc 47A53 |