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)



Examples for the nonlocally convex three space problem

Author: M. Ribe
Journal: Proc. Amer. Math. Soc. 73 (1979), 351-355
MSC: Primary 46A10
MathSciNet review: 518518
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A simple way to obtain certain examples of locally bounded spaces E of the following kind is described: E is nonlocally convex but contains a locally convex subspace K such that $ E/K$ is locally convex.

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

  • [1] S. Dierolf, Über Vererbbarkeitseigenschaften in topologischen Vektorräumen, Dissertation, Munich 1974.
  • [2] Per Enflo, Joram Lindenstrauss, and Gilles Pisier, On the “three space problem”, Math. Scand. 36 (1975), no. 2, 199–210. MR 0383047
  • [3] N. J. Kalton, Basic sequences in 𝐹-spaces and their applications, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), no. 2, 151–167. MR 0415259
  • [4] -, Quotients of F-spaces (to appear).
  • [5] -, The three space problem for locally bounded spaces (to appear).
  • [6] N. J. Kalton and N. T. Peck, Quotients of $ {L^p}(0,1)$ for $ 0 < p < 1$, Notices Amer. Math. Soc. 24 (1977), p. A-115; (to appear).
  • [7] M. Ribe, On the separation properties of the duals of general topological vector spaces, Ark. Mat. 9 (1971), 279–302. MR 0324358
  • [8] M. Ribe, Necessary convexity conditions for the Hahn-Banach theorem in metrizable spaces, Pacific J. Math. 44 (1973), 715–732. MR 0324359
  • [9] James W. Roberts, A nonlocally convex 𝐹-space with the Hahn-Banach approximation property, Banach spaces of analytic functions (Proc. Pelczynski Conf., Kent State Univ., Kent, Ohio, 1976) Springer, Berlin, 1977, pp. 76–81. Lecture Notes in Math., Vol. 604. MR 0625305

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A10

Retrieve articles in all journals with MSC: 46A10

Additional Information

Keywords: Locally bounded space, quotient space, three space problem, dual-separation
Article copyright: © Copyright 1979 American Mathematical Society