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Köthe's example of an incomplete LB-space


Authors: J. Kucera and K. McKennon
Journal: Proc. Amer. Math. Soc. 93 (1985), 79-80
MSC: Primary 46A12; Secondary 46M40
DOI: https://doi.org/10.1090/S0002-9939-1985-0766531-1
MathSciNet review: 766531
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Abstract: The inductive limit of reflexive Banach spaces is fast complete. But the inductive limit of reflexive Fréchet spaces may not be fast complete. Also, an example of a complete, reflexive, nuclear space with a quotient space which is not fast complete is given.


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

  • [1] G. Köthe, Topological vector spaces. I, Springer, Berlin and New York, 1969. MR 0248498 (40:1750)
  • [2] H. Schaefer, Topological vector spaces, 3rd ed., Springer, Berlin and New York, 1971. MR 0342978 (49:7722)
  • [3] M. de Wilde, Closed graph theorems and webbed spaces, Pitman, London, 1978.
  • [4] J. Kucera and K. McKennon, Dieudonné-Schwartz theorem on bounded sets in inductive limits, Proc. Amer. Math. Soc. 78 (1980), 366-368. MR 553378 (81d:46007)
  • [5] Qiu Jing Huei, Some results on bounded sets in inductive limits (to appear). MR 855717 (88b:46005)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766531-1
Keywords: LB-space, LF-space, completeness, fast completeness
Article copyright: © Copyright 1985 American Mathematical Society

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