##  [Gelfand–Naimark Theorem](/gelfand-naimark-theorem) 

  ##  [Gelfand–Naimark Theorem](https://puremath.quantumdictionary.io/gelfand-naimark-theorem-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem that every commutative unital C*-algebra A is *-isomorphic to C(X), the algebra of continuous complex-valued functions on a compact Hausdorff space X (the space of characters or maximal ideals of A), via the Gelfand transform; it establishes a duality between the category of commutative unital C*-algebras and the category of compact Hausdorff spaces.

 

 

 

 

 





 

 



 ##  [Gelfand–Naimark Theorem](https://algebra.quantumdictionary.io/gelfand-naimark-theorem-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem that every commutative C*-algebra is isometrically *-isomorphic to C0(X), the algebra of continuous complex-valued functions vanishing at infinity on a locally compact Hausdorff space X (its spectrum), via the Gelfand transform, realizing a duality between spaces and commutative operator algebras.