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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weak $ A$-convex algebras


Author: Allan C. Cochran
Journal: Proc. Amer. Math. Soc. 26 (1970), 73-77
MSC: Primary 46.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0262830-X
MathSciNet review: 0262830
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Abstract: Necessary and sufficient conditions are given in terms of $ E'$ that a weak topology $ w(E,E')$ on an algebra $ E$ be $ A$-convex. The main condition is that each element $ g$ of $ E'$ contain a weakly closed subspace $ L$ of finite codimension such that $ g$ is bounded on all multiplicative translates of $ L$. For weak topologies, $ A$-convexity (which assumes only separate continuity of multiplication) is equivalent to joint continuity of multiplication.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0262830-X
Keywords: $ A$-convex algebra, locally $ m$-convex algebra, weak topology, topological algebra
Article copyright: © Copyright 1970 American Mathematical Society