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Line 1: 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 obtained in the study of operator algebras are phrased in [[Algebra\|algebraic]] terms, while the techniques used are highly analytic.<ref>''Theory of Operator Algebras I'' By Masamichi Takesaki, Springer 2012, p vi</ref> Although itthe 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==

Operator algebra: Difference between revisions