An example for factorization theory in Banach algebras
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- by P. G. Dixon PDF
- Proc. Amer. Math. Soc. 86 (1982), 65-66 Request permission
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 $A$.References
- Frank F. Bonsall and John Duncan, Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York-Heidelberg, 1973. MR 0423029
- P. G. Dixon, Automatic continuity of positive functionals on topological involution algebras, Bull. Austral. Math. Soc. 23 (1981), no. 2, 265–281. MR 617069, DOI 10.1017/S0004972700007127
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 65-66
- MSC: Primary 46H05; Secondary 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1982-0663867-7
- MathSciNet review: 663867