Definition:Banach Algebra

Definition
Let $R$ be either the real numbers $\R$ or the complex numbers $\C$..

Let $A$ be an algebra over $R$ which is also a Banach space.

Then $A$ is a Banach algebra :
 * $\forall a, b \in R: \norm {a b} \le \norm a \norm b$

where $\norm {\, \cdot \,}$ denotes the norm on $A$.