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Topological algebras with a given dual


Author: Ajit Kaur Chilana
Journal: Proc. Amer. Math. Soc. 42 (1974), 192-197
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1974-0328590-2
MathSciNet review: 0328590
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Abstract: Given an algebra E and a total subspace $ E'$ of its algebraic dual, we obtain necessary and sufficient conditions in terms of $ E'$ for the existence of an A-convex or a locally m-convex topology on E compatible with duality $ (E,E')$. It has also been proved that if E with the weak topology $ w(E,E')$ is the closed linear hull of a bounded set and has hypocontinuous multiplication then it is locally m-convex.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328590-2
Keywords: (right, left) A-convex algebra, locally m-convex algebra, topology compatible with duality, (right, left) multiplicative translate of a functional, collectionwise multiplicative set of functionals, collectionwise (right, left) multiplicative-translation invariant set of functionals, hypocontinuous and jointly continuous multiplication
Article copyright: © Copyright 1974 American Mathematical Society

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