Fredholm operator
A Fredholm operator is a bounded operator between Banach spaces
that has a finite dimensional kernel and cokernel (and closed range).
Equivalently, it is invertible
modulo compact operators
.
That is, if is a Fredholm operator between two vector spaces
and ,
then there exists a bounded operator such that
(1) |
where denotes the space of compact operators on .
(Another way to say this is that is invertible in the Calkin algebra).
The set of Fredholm operators is an open subset of the Banach algebra of bounded operators .
If is Fredholm then so is its adjoint, .
If is a compact operator then is also Fredholm.
Title | Fredholm operator |
---|---|
Canonical name | FredholmOperator |
Date of creation | 2013-03-22 12:58:52 |
Last modified on | 2013-03-22 12:58:52 |
Owner | mhale (572) |
Last modified by | mhale (572) |
Numerical id | 15 |
Author | mhale (572) |
Entry type | Definition |
Classification | msc 47A53 |
Related topic | FredholmIndex |