Cohen–Hewitt factorization theorem

In mathematics, the Cohen–Hewitt factorization theorem states that if [math]\displaystyle{ V }[/math] is a left module over a Banach algebra [math]\displaystyle{ B }[/math] with a left approximate unit [math]\displaystyle{ (u_{i})_{i \in I} }[/math], then an element [math]\displaystyle{ v }[/math] of [math]\displaystyle{ V }[/math] can be factorized as a product [math]\displaystyle{ v = b w }[/math] (for some [math]\displaystyle{ b \in B }[/math] and [math]\displaystyle{ w \in V }[/math]) whenever [math]\displaystyle{ \displaystyle \lim_{i \in I} u_{i} v = v }[/math]. The theorem was introduced by Paul Cohen (1959) and Edwin Hewitt (1964).

References

• "Factorization in group algebras", Duke Mathematical Journal 26 (2): 199–205, 1959, doi:10.1215/s0012-7094-59-02620-1 
• "The ranges of certain convolution operators", Mathematica Scandinavica 15: 147–155, 1964, doi:10.7146/math.scand.a-10738