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