Definition:Unital Banach Algebra

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

Let $\struct {A, \norm \cdot}$ be a Banach algebra over $\Bbb F$ that is unital as an algebra and:
 * $A \ne \set { {\mathbf 0}_A}$

Let ${\mathbf 1}_A$ be the identity element of $A$.

We say that $A$ is a unital Banach algebra :


 * $\norm {\mathbf 1_A} = 1$