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Proceedings of the American Mathematical Society

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An example for factorization theory in Banach algebras

Author: P. G. Dixon
Journal: Proc. Amer. Math. Soc. 86 (1982), 65-66
MSC: Primary 46H05; Secondary 46J15
MathSciNet review: 663867
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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$.

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Keywords: Banach algebra, actorization
Article copyright: © Copyright 1982 American Mathematical Society