The Model Algebra
For any locally compact Hausdorff topological space X, the space C0(X) of continuous complex-valued functions on X which vanish at infinity is in a natural way a commutative C*-algebra:
- The structure of algebra over the complex numbers is obtained by considering the pointwise operations of addition and multiplication.
- The involution is pointwise complex conjugation.
- The norm is the uniform norm on functions.
Note that A is unital if and only if X is compact, in which case C0(X) is equal to C(X), the algebra of all continuous complex-valued functions on X.
Read more about this topic: Gelfand Representation
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