Fredholm operator

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. 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 T : X → Y between two Banach spaces with finite-dimensional kernel ker ⁡ T {displaystyle ker T} and (algebraic) cokernel c o k e r T = Y / r a n T {displaystyle mathrm {coker} ,T=Y/mathrm {ran} ,T} , and with closed range r a n T {displaystyle mathrm {ran} ,T} . The last condition is actually redundant. Equivalently, an operator T : X → Y is Fredholm if it is invertible modulo compact operators, i.e., if there exists a bounded linear operator