Inductive limits of 𝐴-convex algebras

Cochran, Allan C.

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

Inductive limits of $A$-convex algebras
HTML articles powered by AMS MathViewer

by Allan C. Cochran

Proc. Amer. Math. Soc. 37 (1973), 489-496

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

PDF | 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.

References

G. R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc. (3) 15 (1965), 399–421. MR 176344, DOI 10.1112/plms/s3-15.1.399
Richard Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455–471. MR 51445
R. Creighton Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95–104. MR 105611
A. C. Cochran, R. Keown, and C. R. Williams, On a class of topological algebras, Pacific J. Math. 34 (1970), 17–25. MR 273399
Allan C. Cochran, Weak $A$-convex algebras, Proc. Amer. Math. Soc. 26 (1970), 73–77. MR 262830, DOI 10.1090/S0002-9939-1970-0262830-X
Allan C. Cochran, Topological algebras and Mackey topologies, Proc. Amer. Math. Soc. 30 (1971), 115–119. MR 291807, DOI 10.1090/S0002-9939-1971-0291807-4
Ernest A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952), 79. MR 51444
Ju-kwei Wang, Multipliers of commutative Banach algebras, Pacific J. Math. 11 (1961), 1131–1149. MR 138014
Seth Warner, Weak locally multiplicatively-convex algebras, Pacific J. Math. 5 (1955), 1025–1032. MR 76295
Seth Warner, Inductive limits of normed algebras, Trans. Amer. Math. Soc. 82 (1956), 190–216. MR 79226, DOI 10.1090/S0002-9947-1956-0079226-3
Seth Warner, Bornological structures, Illinois J. Math. 4 (1960), 231–245. MR 110939