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Proceedings of the American Mathematical Society

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



Inductive limits of $ A$-convex algebras

Author: Allan C. Cochran
Journal: Proc. Amer. Math. Soc. 37 (1973), 489-496
MSC: Primary 46H20
MathSciNet review: 0310639
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Abstract: The ideas of inductive limits and bornological spaces are extended to A-convex algebras. The usual locally convex linear space characterization of bornological spaces has an appropriate analog for A-convex algebras. The results here have a strong connection to locally m-convex algebras (A-convexity generalizes m-convexity) and some additional information relating to m-convex algebras is given. Comparisons of various inductive limits are obtained including results which insure that these limits coincide. Finally, A-bornological algebras are introduced and studied. It is shown that the property of being A-bornological is preserved with respect to several general constructions.

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Keywords: A-convex algebra, m-convex algebra, bornological space, normed algebra, inductive limit of algebras, Mackey topology
Article copyright: © Copyright 1973 American Mathematical Society