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Uniqueness of topology for semisimple $ {\rm LFQ}$-algebras


Author: Maria Fragoulopoulou
Journal: Proc. Amer. Math. Soc. 117 (1993), 963-969
MSC: Primary 46H20
DOI: https://doi.org/10.1090/S0002-9939-1993-1101981-X
MathSciNet review: 1101981
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Abstract: Various classes of semisimple lmc algebras, among them barrelled Pták $ Q$-algebras, $ LFQ$-algebras, and $ FQ$-algebras, have a uniquely determined topology.


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  • 1. B. Aupetit, The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras, J. Funct. Anal. 47 (1982), 1-6. MR 663830 (83g:46044)
  • [1] F. F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, Berlin, Heidelberg, and New York, 1973. MR 0423029 (54:11013)
  • [2] R. M. Brooks, Analytic structure in the spectrum of a natural system, Pacific J. Math. 49 (1973), 315-334. MR 0361792 (50:14237)
  • [3] R. L. Carpender, Uniqueness of topology for commutative semisimple $ F$-algebras, Proc. Amer. Math. Soc. 29 (1971), 113-117. MR 0298424 (45:7476)
  • [4] P. Pérez Carreras and J. Bonet, Barrelled locally convex spaces, North-Holland, Amsterdam, 1987. MR 880207 (88j:46003)
  • [5] O. Forster, Uniqueness of topology in Stein algebras, Function Algebras, Proc. Internat. Sympos., Tulane Univ. 1965, Scott, Foresman, Glenview, IL, 1966, pp. 157-163. MR 0197772 (33:5935)
  • [6] J. Horváth, Topological vector spaces and distributions, Vol. I, Addison-Wesley, Reading, MA, 1966. MR 0205028 (34:4863)
  • [7] B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73 (1967), 537-539. MR 0211260 (35:2142)
  • [8] G. Köthe, Topological vector spaces. I, Springer-Verlag, Berlin, Heidelberg, and New York, 1969. MR 0248498 (40:1750)
  • [9] -, Topological vector spaces. II, Springer-Verlag, New York, Heidelberg, and Berlin, 1974.
  • [10] R. J. Loy, Uniqueness of the Frechet space topology on certain topological algebras, Bull. Austral. Math. Soc. 4 (1971), 1-7. MR 0298420 (45:7472)
  • [11] A. Mallios, Topological algebras. Selected topics, North-Holland, Amsterdam, 1986. MR 857807 (87m:46099)
  • [12] -, On geometric topological algebras, J. Math. Anal. Appl. (to appear). MR 1200988 (93m:46053)
  • [13] E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc., vol. 11, Amer. Math. Soc., Providence, RI, 1952. MR 0051444 (14:482a)
  • [14] T. J. Ransford, A short proof of Johnson's uniqueness-of-norm theorem, Bull. London Math. Soc. 21 (1989), 487-488. MR 1005828 (90g:46069)
  • [15] Y. Tsertos, Representable and pure states of $ {\ast}$-algebras. A characterization of $ Q$-algebras, preprint.
  • [16] S. Warner, Polynomial completeness in locally multiplicatively-convex algebras, Duke Math. J. 23 (1956), 1-11. MR 0073947 (17:512d)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1101981-X
Keywords: Closed graph pair, barrelled Pták $ Q$-algebra, $ LFQ$-algebra
Article copyright: © Copyright 1993 American Mathematical Society

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