In mathematics, the Cohen–Hewitt factorization theorem states that if

V

is a

left module In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of ''module'' generalizes also the notion of abelian group, since the abelian groups are exactly the ...

over a

Banach algebra In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach ...

B

with a left approximate unit

(u_)_

, then an element

v

V

can be factorized as a product

v = b w

(for some

b \in B

and

w \in V

) whenever

\displaystyle \lim_ u_ v = v

. The theorem was introduced by and .

References

* * Banach algebras Theorems in functional analysis {{analysis-stub