Definition:C*-Algebra

Definition
Let $\Bbb F \in \set {\R, \C}$.

Let $A$ be a Banach algebra over $\Bbb F$.

Let $A$ have a conjugate-linear anti-automorphic involution $*$ satisfying the following axioms:

Then $A$ is referred to as a $\text C^*$-algebra.

Also known as
An older term for $C^*$-algebra is $B^*$-algebra.