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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Algèbres $ A$-convexes et problème de Michael


Authors: M. Akkar, L. Oubbi and M. Oudadess
Journal: Proc. Amer. Math. Soc. 110 (1990), 97-101
MSC: Primary 46H05
MathSciNet review: 1014641
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Abstract: We give an example of a locally $ A$-convex algebra which is neither $ m$-convex nor uniformly $ A$-convex. This example is used to answer some questions on $ A$-convex algebras (see symbol 4). We especially show that Michael's problem (in $ m$-convex algebras) is equivalent to the same problem in $ A$-convex algebras. Finally some questions on bounded sets in $ A$-convex algebras are studied.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1014641-8
PII: S 0002-9939(1990)1014641-8
Keywords: Locally $ A$-convex algebras, locally multiplicatively convex algebras, bounded sets, Michael Problem
Article copyright: © Copyright 1990 American Mathematical Society