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.


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.


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