Timeline for Do subalgebras of C(X) admit a description in terms of the compact Hausdorff space X?
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| Dec 5, 2011 at 23:45 | comment | added | Peter Arndt | @Buschi Sergio: Well, the finitely generated subalgebra is a quotient of a polynomial algebra and thus corresponds to an affine variety. The spectrum of the C*-algebra A is given by the characters A-->C and precomposition with the inclusion map, whether it is *-respecting or not, gives a surjective ring map to a field, hence a maximal ideal. This defines a map from the points of the compact Hausdorff space to the affine variety (whose points correspond to maximal ideals). | |
| Dec 5, 2011 at 18:47 | comment | added | Buschi Sergio | Forgive me, I'm no too clever, but $C(X)$ isnt a polynomial algebra, then I dont understnd your assetion. | |
| Dec 5, 2011 at 17:11 | history | answered | Andreas Thom | CC BY-SA 3.0 |