C*-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.