Geodesic
Complete Sets of Observables and Pure States
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1276-1280

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Gudder, Stanley P. Complete Sets of Observables and Pure States. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1276-1280. doi: 10.4153/CJM-1968-125-0
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[4] 4. 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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