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Example of an algebra which is nontopologizable as a locally convex topological algebra


Author: W. Żelazko
Journal: Proc. Amer. Math. Soc. 110 (1990), 947-949
MSC: Primary 46H05; Secondary 46J05
DOI: https://doi.org/10.1090/S0002-9939-1990-1012942-0
MathSciNet review: 1012942
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Abstract: Let $ X$ be a real or complex linear space and denote by $ L(X)$ the algebra of all its endomorphisms. We prove that $ L(X)$ is topologizable as a locally convex topological algebra (with jointly continuous multiplication) if and only if it is topologizable as a Banach algebra and this holds if and only if $ X$ is of finite dimension.


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

  • [1] E. Beckenstein, L. Narici and C. Suffel, Topological algebras, North-Holland, Amsterdam, 1977. MR 0473835 (57:13495)
  • [2] A. Mallios, Topological algebras. Selected topics, North-Holland, Amsterdam, 1986. MR 857807 (87m:46099)
  • [3] L. Waelbroeck, Topological vector spaces and algebras, Lecture Notes in Math., vol. 230, Springer-Verlag, Berlin, 1971. MR 0467234 (57:7098)
  • [4] W. Żelazko, Selected topics in topological algebras, Aarhus University Lecture Notes, vol. 31, 1971.
  • [5] -, O pewnych otwartych problemach teorii algebr topologicznych, Proc. Conf. Szczecin, 1988, in print.
  • [6] -, On certain open problems in topological algebras, Rend. Sem. Mat. Fis. Milano, in print.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1012942-0
Keywords: Locally convex algebras, topologization of an algebra
Article copyright: © Copyright 1990 American Mathematical Society

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