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C*-algebras and Mackey's axioms

C*-algebras and Mackey's axioms
C*-algebras and Mackey's axioms
A non-commutative version of probability theory is outlined, based on the concept of a ?*-algebra of operators (sequentially weakly closed C*-algebra of operators). Using the theory of ?*-algebras, we relate the C*-algebra approach to quantum mechanics as developed by Kadison with the probabilistic approach to quantum mechanics as axiomatized by Mackey. The ?*-algebra approach to quantum mechanics includes the case of classical statistical mechanics; this important case is excluded by the W*-algebra approach. By considering the ?*-algebra, rather than the von Neumann algebra, generated by the given C*-algebra A in its reduced atomic representation, we show that a difficulty encountered by Guenin concerning the domain of a state can be resolved.
0010-3616
132-146
Plymen, Roger J.
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Plymen, Roger J.
76de3dd0-ddcb-4a34-98e1-257dddb731f5

Plymen, Roger J. (1968) C*-algebras and Mackey's axioms. Communications in Mathematical Physics, 8 (2), 132-146. (doi:10.1007/BF01645801).

Record type: Article

Abstract

A non-commutative version of probability theory is outlined, based on the concept of a ?*-algebra of operators (sequentially weakly closed C*-algebra of operators). Using the theory of ?*-algebras, we relate the C*-algebra approach to quantum mechanics as developed by Kadison with the probabilistic approach to quantum mechanics as axiomatized by Mackey. The ?*-algebra approach to quantum mechanics includes the case of classical statistical mechanics; this important case is excluded by the W*-algebra approach. By considering the ?*-algebra, rather than the von Neumann algebra, generated by the given C*-algebra A in its reduced atomic representation, we show that a difficulty encountered by Guenin concerning the domain of a state can be resolved.

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More information

Published date: June 1968
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 359973
URI: https://eprints.soton.ac.uk/id/eprint/359973
ISSN: 0010-3616
PURE UUID: a686b9e3-1e60-45bb-9fb9-3959363fa92f

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Date deposited: 26 Nov 2013 13:51
Last modified: 18 Jul 2017 03:16

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