State (Functional Analysis): Functional Analysis, C*-Algebra, Positive Linear Functional, Operator Norm, Convex Set, Probability Measure - Tapa blanda

State (Functional Analysis)

Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In functionalanalysis, a state on a C\*-algebra is a positive linear functional ofnorm 1. The set of states of a C\*-algebra A, sometimes denoted by S(A)is always a convex set. The extremal points of S(A) are called purestates. If A has a multiplicative identity, S(A) is compact in theweak\*-topology. In the C\*-algebraic formulation of quantum mechanicsstates in this previous sense correspond to physical states, i.e.mappings from physical observables to their expected measurementoutcome.States can be viewed as noncommutative generalizations ofprobability measures. By Gelfand representation, every commutativeC\*-algebra A is of the form C0(X) for some locally compact Hausdorff X.In this case, S(A) consists of positive Radon measures on X, and thepure states are the evaluation functionals on X. A bounded linearfunctional on a C\*-algebra A is said to be self-adjoint if it isreal-valued on the self-adjoint elements of A. Self-adjoint functionalsare noncommutative analogues of signed measures.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 80 pp. Englisch. Nº de ref. del artículo: 9786131245145

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