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
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.
|Date of creation||2013-03-22 12:58:52|
|Last modified on||2013-03-22 12:58:52|
|Last modified by||mhale (572)|