KnowraCompact operatorLinked fromLinked fromThe 9 pages that link to Compact operator, each with the reason it gives.All 9Broader topic 2Related 5Narrower topic 2Functional analysisBroader topic: Compactness restores parts of finite-dimensional spectral behavior in infinite dimensions.Fredholm operatorRelated: Compact perturbations preserve Fredholmness and leave the index unchanged.Spectral theoremRelated: Compact self-adjoint operators admit an orthonormal eigenbasis after accounting for the kernel.Fredholm alternativeNarrower topic: Compactness is the hypothesis that makes identity-perturbed operators obey the alternative.Schauder fixed-point theoremRelated: Compactness of the image often supplies the compact set needed for Schauder’s theorem.Operator theoryBroader topic: Compactness makes infinite-dimensional spectral behavior resemble finite-dimensional linear algebra.Fredholm theoryNarrower topic: Compact perturbations preserve Fredholmness and leave the index unchanged.Fredholm's theoremRelated: Compact perturbations of the identity provide the standard setting for the theorem.Riesz's lemmaRelated: Riesz's lemma helps show the identity operator on an infinite-dimensional normed space is not compact.