: Mathématiques: Fredholm operator

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Fredholm operator

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 ${\\displaystyle \\ker T}$ and finite-dimensional (algebraic) cokernel ${\\displaystyle \\mathrm {coker} \\,T=Y/\\mathrm {ran} \\,T}$ , and with closed range ${\\displaystyle \\mathrm {ran} \\,T}$ . The last condition is actually redundant.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Fredholm_operator)