Cohen–Hewitt factorization theorem

In mathematics, the Cohen–Hewitt factorization theorem states that if $$ V $$ is a left module over a Banach algebra $$ B $$ with a left approximate unit $$ (u_{i})_{i \in I} $$, then an element $$ v $$ of $$ V $$ can be factorized as a product $$ v = b w $$ (for some $$ b \in B $$ and $$ w \in V $$) whenever $$ \displaystyle \lim_{i \in I} u_{i} v = v $$. The theorem was introduced by and.