NationMaster - Encyclopedia: State (functional analysis)

In functional analysis, a state on a C*-algebra is a positive linear functional of norm 1. The set of states on a C*-algebra A with identity is a compact convex set in the weak*-topology.

In the C*-algebraic formulation of quantum mechanics, states in this previous sense correspond to physical states.

See also:

pure state

GNS construction

Quantum mechanics

Results from FactBites:

McClamrock: Functional Analysis and Etiology (3506 words)
	The heart's function as blood circulator contributes to the survival of species that have hearts, and thus is part of the explanation of the presence of hearts in current organisms.
	Functional analysis is not then underdescribed deductive-nomological explanation for the presence of the analyzed structure, but it may still be a central part of an (evolutionary) explanation of the presence of that structure.
	What this example shows is that functional analysis can properly be carried on in biology quite independently of evolutionary considerations: a complex capacity of an organism (or one of its parts or systems) may be explained by appeal to a functional analysis regardless of how it relates to the organism's capacity to maintain the species.

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