Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Representation of $ A$-convex algebras


Author: Allan C. Cochran
Journal: Proc. Amer. Math. Soc. 41 (1973), 473-479
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1973-0333735-3
MathSciNet review: 0333735
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Algebraic properties of $ A$-convex algebras are developed via a functor to locally $ m$-convex algebras. The Gel'fand-Mazur theorem holds for $ A$-convex algebras, and this fact allows a Gel'fand-type representation theorem for a subclass of uniformly $ A$-convex algebras. Connections to existing functional representation theory are also obtained.


References [Enhancements On Off] (What's this?)

  • [1] A. C. Cochran, R. Keown and C. R. Williams, On a class of topological algebras, Pacific J. Math. 34 (1970), 17-25. MR 42 #8278. MR 0273399 (42:8278)
  • [2] A. C. Cochran, Topological algebras and Mackey topologies, Proc. Amer. Math. Soc. 30 (1971), 115-119. MR 45 #897. MR 0291807 (45:897)
  • [3] -, Inductive limits of $ A$-convex algebras, Proc. Amer. Math. Soc. 37 (1973), 489-496. MR 0310639 (46:9737)
  • [4] A. Mallios, On functional representations of topological algebras, J. Functional Analysis 6 (1970), 468-480. MR 42 #5047. MR 0270154 (42:5047)
  • [5] E. A. Michael, Locally multiplicatively-convex algebras, Mem. Amer. Math. Soc. no. 11 (1952). MR 14, 482. MR 0051444 (14:482a)
  • [6] P. D. Morris and D. E. Wulbert, Functional representation of topological algebras, Pacific J. Math. 22 (1967), 323-337. MR 35 #4730. MR 0213876 (35:4730)
  • [7] M. A. Naĭmark, Normed rings, rev. ed., GITTL, Moscow, 1956; English transl., Noordhoff, Groningen, 1964. MR 19, 870; 34 #4928.
  • [8] P. Turpin, Une remarque sur les algèbres à inverse continu, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1686-A1689. MR 42 #3571. MR 0268674 (42:3571)
  • [9] L. Waelbrock, Topological vector spaces and algebras, Lecture Notes in Math., no. 230, Springer-Verlag, Berlin and New York, 1971. MR 0467234 (57:7098)
  • [10] J. Wang, Multipliers of commutative Banach algebras, Pacific J. Math. 11 (1961), 1131-1149. MR 25 #1462. MR 0138014 (25:1462)
  • [11] S. Warner, Inductive limits of normed algebras, Trans. Amer. Math. Soc. 82 (1956), 190-216. MR 18, 52. MR 0079226 (18:52e)
  • [12] -, The topology of compact convergence on continuous function spaces, Duke Math. J. 25 (1958), 265-282. MR 21 #1521. MR 0102735 (21:1521)
  • [13] J. H. Williamson, On topologizing the field $ C(t)$, Proc. Amer. Math. Soc. 5 (1954), 729-734. MR 16, 145. MR 0063574 (16:145f)
  • [14] W. Zelazko, On generalized topological divisors of zero in $ m$-convex locally convex algebras, Studia Math. 28 (1966), 9-16. MR 34 #3362. MR 0203512 (34:3362)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46H05

Retrieve articles in all journals with MSC: 46H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0333735-3
Keywords: $ A$-convex algebra, locally $ m$-convex algebra, Gel'fand-Mazur theorem, strict topology, compact-open topology, Gel'fand representation theorem
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society