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

Language: English

Published by Omniscriptum, 2026

6131245142 / 9786131245145

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nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In functional analysis, a state on a C -algebra is a positive linear functional of norm 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 pure states. If A has a multiplicative identity, S(A) is compact in the weak -topology. In the C -algebraic formulation of quantum mechanics, states in this previous sense correspond to physical states, i.e. mappings from physical observables to their expected measurement outcome.States can be viewed as noncommutative generalizations of probability measures. By Gelfand representation, every commutative C -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 the pure states are the evaluation functionals on X. A bounded linear functional on a C -algebra A is said to be self-adjoint if it is real-valued on the self-adjoint elements of A. Self-adjoint functionals are noncommutative analogues of signed measures.…

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Bibliographic details

Title
State (Functional Analysis) : Functional Analysis, C\*-Algebra, Positive Linear Functional, Operator Norm, Convex Set, Probability Measure
Author
Mariam T. Tennoe
Publisher
Omniscriptum
Publication year
2026
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
6131245142
ISBN 13
9786131245145
Item weight
137 grams
Dimensions
220x150x5 mm

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