Properties of States
- a tracial state is a state such that
For any separable C*-algebra, the set of tracial states is a Choquet simplex).
- a state is called normal, iff for every monotone, increasing net of operators with upper bound, converges to .
- a state is said to be faithful, if the image of strictly positive operators is itself strictly positive
Read more about this topic: State (functional Analysis)
Famous quotes containing the words properties of, properties and/or states:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The genius of the United States is not best or most in its executives or legislatures, nor in its ambassadors or authors or colleges, or churches, or parlors, nor even in its newspapers or inventors, but always most in the common people.”
—Walt Whitman (1819–1892)