High Quality Content by WIKIPEDIA articles! In mathematics, a Fredholm operator is an operator that arises in the Fredholm theory of integral equations. It is named in honour of Erik Ivar Fredholm. A Fredholm operator is a bounded linear operator between two Banach spaces whose kernel and cokernel are finite-dimensional and whose range is closed. (The last condition is actually redundant.[1]) Equivalently, an operator T : X -> Y is Fredholm if it is invertible modulo compact operators. The set of Fredholm operators from X to Y is open in the Banach space L(X, Y) of bounded linear operators, equipped with the operator norm. More precisely, when T0 is Fredholm from X to Y, there exists > 0 such that every T in L(X, Y) with ||T – T0|| < is Fredholm, with the same index as that of T0.

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