Definition 28.1.2 (Unital Banach Algebra).label Let $A$ be a Banach algebra, then $A$ is unital if there exists $1 \in A$ such that for any $x \in A$, $x1 = 1x = x$. In which case, $1$ is the unique multiplicative identity of $A$.
Definition 28.1.2 (Unital Banach Algebra).label Let $A$ be a Banach algebra, then $A$ is unital if there exists $1 \in A$ such that for any $x \in A$, $x1 = 1x = x$. In which case, $1$ is the unique multiplicative identity of $A$.