Timeline for When is $A : C(X) \to C(Y)$ a composition operator?
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| Dec 5, 2009 at 1:29 | comment | added | Oleg Eroshkin | I don't remember if there are examples of hemicompact spaces (without k-space propery) such that $M(C(X))\neq X$ (I don't have Goldmann's book at home). Here, $M(C(X))$ is the space of all continuous homomorphisms of the algebra $C(X)$ to ℂ. It seems, that $C(M(C(X)))=C(X)$ (is it?). Then try $Y=M(C(X))$ and identity maps between $C(X)$ and $C(Y)$. | |
| Dec 4, 2009 at 23:39 | comment | added | santker heboln | Ok, thanks. I looked it up. That is a very neat trick and it answers my question, but if we drop the k-space hypothesis the original approach doesn't work anymore. I would still like to see a counterexample or alternative proof in this case. | |
| Dec 4, 2009 at 20:44 | history | answered | Oleg Eroshkin | CC BY-SA 2.5 |