Geodesic
Excising States of C*-Algebras
Canadian journal of mathematics, Tome 38 (1986) no. 5, pp. 1239-1260

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

A net {aα } of positive, norm one elements of a C*-algebra A excises a state f of A if This notion has been used explicitly by the second author [4, 5, 6] for pure states, but the present paper will explore it more fully. The name is motivated by the following example. Let K be the unit disk in the complex plane, A = C(K) and f(a) = a(0). Define an(reiθ) = φn(r), where Note that the sets {t ∊ K:an(t) ∊ 0} form rings about 0 with radii tending to 0. In this sense the sequence {an } “cuts out” the state f and, in the limit, isolates it from all other states. 
Akemann, Charles A.; Anderson, Joel; Pedersen, Gert K. Excising States of C*-Algebras. Canadian journal of mathematics, Tome 38 (1986) no. 5, pp. 1239-1260. doi: 10.4153/CJM-1986-063-7
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