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).

References

• Cohen, Paul J. (1959), "Factorization in group algebras", Duke Mathematical Journal, 26 (2): 199–205, doi:10.1215/s0012-7094-59-02620-1, MR 0104982
• Hewitt, Edwin (1964), "The ranges of certain convolution operators", Mathematica Scandinavica, 15: 147–155, doi:10.7146/math.scand.a-10738, MR 0187016
• Mortini, Raymond (May 2019), "A Simpler Proof of Cohen's Factorization Theorem", The American Mathematical Monthly, 126 (5): 459–463