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 $v=bw$ (for some $b\in B$ and $w\in V$ ) whenever $\displaystyle \lim _{i\in I}u_{i}v=v$ . The theorem was introduced by Paul Cohen (1959) and Edwin Hewitt (1964).