properties of states
Let be a -algebra (http://planetmath.org/CAlgebra) and .
Let and denote the state (http://planetmath.org/State) space and the pure state space of , respectively.
The space is sufficiently large to reveal many of elements of a -algebra.
0.2 Pure states
The pure state space is also sufficiently large to the of Theorem 1. Hence, we can replace by , or by any other family of linear functionals such that , in the previous result.
Theorem 2 - We have that
separates points, i.e. if and only if for all .
is if and only if for all .
is positive if and only if for all .
If is , then for some .
- Every multiplicative linear functional on is a pure state.
|Title||properties of states|
|Date of creation||2013-03-22 17:45:24|
|Last modified on||2013-03-22 17:45:24|
|Last modified by||asteroid (17536)|