Gelfand Representation - The C*-algebra Case

The C*-algebra Case

As motivation, consider the special case A = C0(X). Given x in X, let be pointwise evaluation at x, i.e. . Then is a character on A, and it can be shown that all characters of A are of this form; a more precise analysis shows that we may identify ΦA with X, not just as sets but as topological spaces. The Gelfand representation is then an isomorphism

Read more about this topic:  Gelfand Representation

Famous quotes containing the word case:

    “Never in any case say I have lost such a thing, but I have returned it. Is your child dead? It is a return. Is your wife dead? It is a return. Are you deprived of your estate? Is not this also a return?”
    —Epictetus (c. 55–135)