Gelfand–Naimark–Segal construction

In functional analysis, a discipline within mathematics, given a C ∗ {\displaystyle C^{*}} -algebra A {\displaystyle A} , the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic ∗ {\displaystyle *} -representations of A {\displaystyle A} and certain linear functionals on A {\displaystyle A} (called states). The correspondence is shown by an explicit construction of the ∗ {\displaystyle *} -representation from the state.

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