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==Overview==
Operator algebras can be used to study arbitrary sets of operators with little algebraic relation ''simultaneously''. From this point of view, operator algebras can be regarded as a generalization of [[spectral theory]] of a single operator. In general, operator algebras are [[noncommutative ring|non-commutative]] [[Ring (mathematics)|rings]].
An operator algebra is typically required to be [[closure (mathematics)|closed]] in a specified operator [[topology]] inside the whole algebra of continuous linear operators. In particular, it is a set of operators with both algebraic and topological closure properties. In some disciplines such properties are [[axiom]]ized and algebras with certain topological structure become the subject of the research.
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