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Topological algebras and Mackey topologies


Author: Allan C. Cochran
Journal: Proc. Amer. Math. Soc. 30 (1971), 115-119
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1971-0291807-4
MathSciNet review: 0291807
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Abstract: Let E be a locally m-convex algebra with dual space $ E'$. In a recent paper S. Warner asked if the finest locally m-convex topology on E compatible with $ E'$ was the mackey topology. It is shown that this is not the case. A similar result is given for this question in the A-convex algebra case. For any A-convex algebra, a construction is given of an associated locally m-convex algebra. It is shown that this associated locally m-convex topology is always the compact-open topology for the space $ {C_b}(S)$ with the strict topology.


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

  • [1] R. F. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455-471. MR 14, 482. MR 0051445 (14:482b)
  • [2] R. C. Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95-104. MR 21 #4350. MR 0105611 (21:4350)
  • [3] A. C. Cochran, C. R. Williams and R. Keown, On a class of topological algebras, Pacific J. Math. 34 (1970), 17-25. MR 0273399 (42:8278)
  • [4] A. C. Cochran, Weak A-convex algebras, Proc. Amer. Math. Soc. 26 (1970), 73-77. MR 0262830 (41:7435)
  • [5] J. B. Conway, The strict topology and compactness in the space of measures, Bull. Amer. Math. Soc. 72 (1966), 75-78. MR 32 #4509. MR 0187054 (32:4509)
  • [6] E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. No. 11 (1952). MR 14, 482. MR 0051444 (14:482a)
  • [7] P. D. Morris and D. E. Wulbert, Functional representations of topological algebras, Pacific J. Math. 22 (1967), 323-337. MR 0213876 (35:4730)
  • [8] S. Warner, Weak locally multiplicatively-convex algebras, Pacific J. Math. 5 (1955), 1025-1032. MR 17, 876. MR 0076295 (17:876e)
  • [9] -, Inductive limits of normed algebras, Trans. Amer. Math. Soc. 82 (1956), 190-216. MR 18, 52. MR 0079226 (18:52e)
  • [10] W. H. Summers, A representation theorem for biequicontinuous completed tensor products of weighted spaces, Trans. Amer. Math. Soc. 146 (1969), 121-131. MR 40 #4748. MR 0251521 (40:4748)
  • [11] J. Wang, Multipliers of commutative Banach algebras, Pacific J. Math. 11 (1961), 1131-1149. MR 0138014 (25:1462)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0291807-4
Keywords: Bornological space, mackey topology, locally m-convex algebra, A-convex algebra, strict topology, compact-open topology
Article copyright: © Copyright 1971 American Mathematical Society

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