Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0262830
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.50

Retrieve articles in all journals with MSC: 46.50

Additional Information

Keywords: $ A$-convex algebra, locally $ m$-convex algebra, weak topology, topological algebra
Article copyright: © Copyright 1970 American Mathematical Society