In mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations. They are named in honour of Erik Ivar Fredholm. By definition, a Fredholm operator is a bounded linear operator T : X → Y between two Banach spaces with finite-dimensional kernel and finite-dimensional (algebraic) cokernel , and with closed range . The last condition is actually redundant.[1]
The index of a Fredholm operator is the integer
or in other words,