The spectral theory of posets and its applications to $C^*$-algebras
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- by A. H. Dooley PDF
- Trans. Amer. Math. Soc. 224 (1976), 143-155 Request permission
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.References
- Horst Behncke, $C^{^*}$-algebras with finite duals, J. Functional Analysis 14 (1973), 253–268. MR 0343046, DOI 10.1016/0022-1236(73)90071-2
- Nicolas Bourbaki, Elements of mathematics. General topology. Part 1, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205210
- Ola Bratteli, Inductive limits of finite dimensional $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234. MR 312282, DOI 10.1090/S0002-9947-1972-0312282-2
- Ola Bratteli, Structure spaces of approximately finite-dimensional $C^{\ast }$-algebras, J. Functional Analysis 16 (1974), 192–204. MR 0348507, DOI 10.1016/0022-1236(74)90063-9 —, Structure spaces of approximately finite-dimensional ${C^\ast }$-algebras. II (preprint, 10 pp.)
- Karl Heinrich Hofmann and Klaus Keimel, A general character theory for partially ordered sets and lattices, Memoirs of the American Mathematical Society, No. 122, American Mathematical Society, Providence, R.I., 1972. MR 0340129 C. Kuratowski, Topologie. Vol. 1, 3rd ed., PWN, Warsaw, 1952. MR 14, 1000.
Additional Information
- © Copyright 1976 American Mathematical Society
- 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