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:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“In the case of a deliberate, palpable, and dangerous exercise of ... powers not granted by the compact, the States ... are in duty bound to interpose for arresting the progress of the evil, and for maintaining within their respective limits the authorities, rights, and liberties appertaining to them.”
—James Madison (1751–1836)