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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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0291807-4
Keywords: Bornological space, mackey topology, locally m-convex algebra, A-convex algebra, strict topology, compact-open topology
Article copyright: © Copyright 1971 American Mathematical Society