\begin{definition}[Definition:Banach Algebra]
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''' {{iff}}:
:$\forall a, b \in R: \norm {a b} \le \norm a \norm b$
where $\norm {\, \cdot \,}$ denotes the norm on $A$.
{{NamedforDef|Stefan Banach|cat = Banach}}
\end{definition}