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 |