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In [[functional analysis]], 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 composition of mappings.
The results are phrased in [[Algebra|algebraic]] terms, while the techniques are highly analytic.<ref>''Theory of Operator Algebras I'' By Masamichi Takesaki, Springer 2012, p vi</ref> Although it 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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