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