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Proceedings of the American Mathematical Society

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



Topological algebras and Mackey topologies

Author: Allan C. Cochran
Journal: Proc. Amer. Math. Soc. 30 (1971), 115-119
MSC: Primary 46H05
MathSciNet review: 0291807
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Abstract: Let E be a locally m-convex algebra with dual space $ E'$. In a recent paper S. Warner asked if the finest locally m-convex topology on E compatible with $ E'$ was the mackey topology. It is shown that this is not the case. A similar result is given for this question in the A-convex algebra case. For any A-convex algebra, a construction is given of an associated locally m-convex algebra. It is shown that this associated locally m-convex topology is always the compact-open topology for the space $ {C_b}(S)$ with the strict topology.

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Keywords: Bornological space, mackey topology, locally m-convex algebra, A-convex algebra, strict topology, compact-open topology
Article copyright: © Copyright 1971 American Mathematical Society

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