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 admission of the States of Wyoming and Idaho to the Union are events full of interest and congratulation, not only to the people of those States now happily endowed with a full participation in our privileges and responsibilities, but to all our people. Another belt of States stretches from the Atlantic to the Pacific.”
—Benjamin Harrison (1833–1901)