Gelfand-Naimark Theorem
The Gelfand-Naimark Theorem is a fundamental result in functional analysis that connects C*-algebras and commutative Banach algebras. It states that every commutative C*-algebra can be represented as a continuous function algebra on a compact Hausdorff space. This means that we can study these algebras through the lens of topology and analysis.
Additionally, the theorem provides a way to understand the structure of C*-algebras by linking them to spectral theory. It shows that every C*-algebra can be represented as a space of continuous functions, allowing mathematicians to apply techniques from topology to analyze algebraic properties.