Mathematics Colloquia and Seminars

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This will be an expository talk on the Gelfand-Naimark Theorem. The C*-algebra C(X) of continuous complex functions on a compact hausdorf space X carries all the information that the topology of X does. For any abelian C*-algebra A one can construct a topological space spec(A) for which A is the algebra of functions on spec(A). This means that abelian C*-algebras and compact hausdorf spaces are pretty much the same things. As a corollary, one obtains a nice characterization of C*(N), the C*-algebra generated by a normal operator N.