: Mathématiques: operator algebra

mathematical analysis > functional analysis > operator algebra

algebra > abstract algebra > algebraic structure > ring theory > operator algebra

operator algebra

In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study of operator algebras are often phrased in algebraic terms, while the techniques used are often highly analytic. 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.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Operator_algebra)

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