The spectral theory of posets and its applications to -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 -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.
- [1] Horst Behncke, 𝐶^{*}-algebras with finite duals, J. Functional Analysis 14 (1973), 253–268. MR 0343046
- [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
- [3] Ola Bratteli, Inductive limits of finite dimensional 𝐶*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234. MR 312282, https://doi.org/10.1090/S0002-9947-1972-0312282-2
- [4] Ola Bratteli, Structure spaces of approximately finite-dimensional 𝐶*-algebras, J. Functional Analysis 16 (1974), 192–204. MR 0348507, https://doi.org/10.1016/0022-1236(74)90063-9
- [5]
-, Structure spaces of approximately finite-dimensional
-algebras. II (preprint, 10 pp.)
- [6] Karl Heinrich Hofmann and Klaus Keimel, A general character theory for partially ordered sets and lattices, American Mathematical Society, Providence, R.I., 1972. Memoirs of the American Mathematical Society, No. 122. MR 0340129
- [7] C. Kuratowski, Topologie. Vol. 1, 3rd ed., PWN, Warsaw, 1952. MR 14, 1000.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1976-0417796-6
Article copyright:
© Copyright 1976
American Mathematical Society