State (functional Analysis)

State (functional Analysis)

In functional analysis, a state on a C*-algebra is a positive linear functional of norm 1. The set of states of a C*-algebra A, sometimes denoted by S(A), is always a convex set. The extremal points of S(A) are called pure states. If A has a multiplicative identity, S(A) is compact in the weak-* topology.

In the C*-algebraic formulation of quantum mechanics, states in this previous sense correspond to physical states, i.e. mappings from physical observables to their expected measurement outcome.