The spectral theory of posets and its applications to 𝐶*-algebras

Dooley, A. H.

doi:10.1090/S0002-9947-1976-0417796-6

The spectral theory of posets and its applications to $C\sp*$ -algebras

Author: A. H. Dooley
Journal: Trans. Amer. Math. Soc. 224 (1976), 143-155
MSC: Primary 46L05; Secondary 06A10
DOI: https://doi.org/10.1090/S0002-9947-1976-0417796-6
MathSciNet review: 0417796
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Abstract: This paper uses methods from the spectral theory of partially ordered sets to clarify and extend some recent results concerning approximately finite-dimensional ${C^\ast}$ -algebras. An extremely explicit description is obtained of the Jacobson topology on the primitive ideal space, and it is shown that this topology has a basis of quasi-compact open sets. In addition, the main results of [4] are proved using only elementary means.

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