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Complete Sets of Observables and Pure States
Published online by Cambridge University Press: 20 November 2018
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It was shown in (1) that a complete set of bounded observables is metrically complete. However, an extra axiom was needed to prove this result (1, footnote, p. 436). In this note we prove the above-mentioned result without the extra axiom. We also show that there is an abundance of pure states if M is closed in the weak topology and give a necessary and sufficient condition for the latter to be the case.
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- Copyright © Canadian Mathematical Society 1968
Footnotes
*
The author is indebted to Harry Mullikin for the proof of part of this theorem.
References
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Varadarajan, V., Probability in physics and a theorem on simultaneous observability, Comm. Pure Appl. Math. 15 (1962), 189–217.Google Scholar
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