# An example for factorization theory in Banach algebras

by P.G.Dixon

*Proc. Amer. Math. Soc.,* **86** (1982), 65-66.

1991 Mathematics Subject Classification: 46H05.

## Abstract

It has been conjectured that, if *A* is a separable Banach algebra in which every element factorizes,
(i.e. for every *x* in *A* there exist *y,z* in *A* with *x* = *yz*), then every pair
of elements in *A* has a common factor. An example is given of a commutative, separable Banach
algebra *A* where the set *M* of elements of *A* which factorize is of codimension one
in *A*, and there exists a pair of elements of *M* with no common factor in *A*.

## Availability

Reprints of the paper available on request: e-mail P.Dixon with extension
@sheffield.ac.uk.

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