Perfect JC-algebras
Perfect C∗-algebras were introduced by Akeman and Shultz in [Perfect C*-algebras, Mem. Amer. Math. Soc. 55(326) (1985)] and they form a certain subclass of C*-algebras determined by their pure states, and for which the general Stone–Weierstrass conjecture is true. In this paper, we introduce the not...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2023-12-01
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| Series: | Bulletin of Mathematical Sciences |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360723500017 |
| Summary: | Perfect C∗-algebras were introduced by Akeman and Shultz in [Perfect C*-algebras, Mem. Amer. Math. Soc. 55(326) (1985)] and they form a certain subclass of C*-algebras determined by their pure states, and for which the general Stone–Weierstrass conjecture is true. In this paper, we introduce the notion of perfect JC-algebras, and we use the strong relationship between a JC-algebra A and its universal enveloping C∗-algebra [Formula: see text], to establish that if [Formula: see text] is perfect and A is of complex type, then A is perfect. It is also shown that every scattered JC-algebra of complex type is perfect, and the same conclusion holds for every JC-algebra of complex type whose primitive spectrum is Hausdorff. |
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| ISSN: | 1664-3607 1664-3615 |