Topological algebras and Mackey topologies

Author:
Allan C. Cochran

Journal:
Proc. Amer. Math. Soc. **30** (1971), 115-119

MSC:
Primary 46H05

DOI:
https://doi.org/10.1090/S0002-9939-1971-0291807-4

MathSciNet review:
0291807

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *E* be a locally *m*-convex algebra with dual space . In a recent paper S. Warner asked if the finest locally *m*-convex topology on *E* compatible with 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 with the strict topology.

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Additional Information

DOI:
https://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