Topological algebras with a given dual

Chilana, Ajit Kaur

doi:10.1090/S0002-9939-1974-0328590-2

Topological algebras with a given dual
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by Ajit Kaur Chilana PDF

Proc. Amer. Math. Soc. 42 (1974), 192-197 Request permission

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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