##  [C\*-Algebra](/c-algebra) 

  ##  [C\*-Algebra](https://algebra.quantumdictionary.io/c-algebra-0) 

  

 [![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

A C*-algebra is a complex Banach *-algebra A equipped with an involution * and a norm satisfying the C*-identity ||a* a|| = ||a||^2 for all a in A; equivalently ||a*|| = ||a|| and the norm is submultiplicative and complete. Unitality is optional and variants include commutative and noncommutative C*-algebras.