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LavaCircus (talk | contribs) Some results in OA are phrased analytically, and some theories use incredibly algebraic proofs. For example subfactor theory often uses fusion categories to prove results. I added "often" twice to the first sentence of the second paragraph. Tags: Mobile edit Mobile web edit |
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In [[functional analysis]], a branch of [[mathematics]], an '''operator algebra''' is an [[algebra over a field|algebra]] of [[continuous function (topology)|continuous]] [[linear operator]]s on a [[topological vector space]], with the multiplication given by the [[function composition|composition of mappings]].
The results obtained in the study of operator algebras are often phrased in [[algebra]]ic terms, while the techniques used are often highly [[mathematical analysis|analytic]].<ref>''Theory of Operator Algebras I'' By [[Masamichi Takesaki]], Springer 2012, p vi</ref> Although the study of operator algebras is usually classified as a branch of functional analysis, it has direct applications to [[representation theory]], [[differential geometry]], [[quantum statistical mechanics]], [[quantum information]], and [[quantum field theory]].
==Overview==
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