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.

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

We say that $A$ is a unital Banach algebra if and only if:

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

Sources

• 2011: Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras ... (previous) ... (next): $4.2$: Definitions and basic examples