In this answer here t.b. writes that $\ell^1(\mathbb Z)$ would then have to be isomorphic to a space of the form $C(K)$ with $K$ compact (metrizable and infinite).
What is the result they are referring to?
Asked
Active
Viewed 79 times
1 Answers
2
Every commutative unital $C^*$ algebra is of the form $C(K)$. This follows from the Gelfand theory. For more references, see here.
voldemort
- 13,385
-
1Additionally, in the case that the $C^*$ algebra is not unital, it is of the form $C_0(X)$ for some locally compact Hausdorff space $X$. – Cameron L. Williams Oct 31 '14 at 23:16