Gelfand–Naimark–Segal construction
CONNECTS CYCLIC *-REPRESENTATIONS OF A AND CERTAIN LINEAR FUNCTIONALS ON A
Gelfand-Naimark-Segal; GNS construction; GNS theorem; Gelfand-Naimark-Segal construction; Gelfand–Naimark–Segal; *-representation
In functional analysis, a discipline within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain linear functionals on A (called states). The correspondence is shown by an explicit construction of the *-representation from the state.