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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $Eā€™$ that a weak topology $w(E,Eā€™)$ on an algebra $E$ be $A$-convex. The main condition is that each element $g$ of $Eā€™$ 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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Keywords: <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$A$">-convex algebra, locally <IMG WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$m$">-convex algebra, weak topology, topological algebra
Article copyright: © Copyright 1970 American Mathematical Society