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.
Read more about State (functional Analysis): Jordan Decomposition, Properties of States
Famous quotes containing the word state:
“That popular fable of the sot who was picked up dead-drunk in the street, carried to the duke’s house, washed and dressed and laid in the duke’s bed, and, on his waking, treated with all obsequious ceremony like the duke, and assured that he had been insane, owes its popularity to the fact that it symbolizes so well the state of man, who is in the world a sort of sot, but now and then wakes up, exercises his reason and finds himself a true prince.”
—Ralph Waldo Emerson (1803–1882)