Inductive limits of -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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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1973-0310639-3

Keywords:
*A*-convex algebra,
*m*-convex algebra,
bornological space,
normed algebra,
inductive limit of algebras,
Mackey topology

Article copyright:
© Copyright 1973
American Mathematical Society