Inductive limits of 𝐴-convex algebras

Cochran, Allan C.

doi:10.1090/S0002-9939-1973-0310639-3

Inductive limits of $A$-convex algebras
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Proc. Amer. Math. Soc. 37 (1973), 489-496 Request permission

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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