Cohen–Hewitt factorization theorem

Short description: Theorem of mathematics

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 $\underset{i\in I}{\lim }{u}_{i}v=v$. 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 
• Mortini, Raymond (May 2019), "A Simpler Proof of Cohen’s Factorization Theorem", The American Mathematical Monthly 126 (5): 459-463, https://www.jstor.org/stable/48662324