An example for factorization theory in Banach algebras
Proc. Amer. Math. Soc., 86 (1982), 65-66.
1991 Mathematics Subject Classification: 46H05.
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.
Reprints of the paper available on request: e-mail P.Dixon with extension
Other publications by P. G. Dixon. Return to P. G. Dixon home page