We present a simpler proof than the original of P. J. Cohen’s factorization theorems for nonunital Banach algebras with an approximate identity. The Monthly publishes articles, as well as notes and ...

In this note we shall generalize the Paley-Wiener theorem to self-adjoint operators similar to (−id/dx). By using a simple factorization result, it is shown that the Paley-Wiener theorem holds if Γ′ ...