Diffuse sequences and perfect 𝐶*-algebras

Akemann, Charles A.; Anderson, Joel; Pedersen, Gert K.

doi:10.1090/S0002-9947-1986-0860391-1

Diffuse sequences and perfect $C^ \ast$-algebras
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by Charles A. Akemann, Joel Anderson and Gert K. Pedersen

Trans. Amer. Math. Soc. 298 (1986), 747-762

DOI: https://doi.org/10.1090/S0002-9947-1986-0860391-1

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Abstract:

The concept of a diffuse sequence in a ${C^{\ast }}$-algebra is introduced and exploited to complete the classification of separable, perfect ${C^{\ast }}$-algebras. A ${C^{\ast }}$-algebra is separable and perfect exactly when the closure of the pure state space consists entirely of atomic states.

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