Examples for the nonlocally convex three space problem
HTML articles powered by AMS MathViewer
- by M. Ribe PDF
- Proc. Amer. Math. Soc. 73 (1979), 351-355 Request permission
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
-
S. Dierolf, Über Vererbbarkeitseigenschaften in topologischen Vektorräumen, Dissertation, Munich 1974.
- Per Enflo, Joram Lindenstrauss, and Gilles Pisier, On the “three space problem”, Math. Scand. 36 (1975), no. 2, 199–210. MR 383047, DOI 10.7146/math.scand.a-11571
- N. J. Kalton, Basic sequences in $F$-spaces and their applications, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), no. 2, 151–167. MR 415259, DOI 10.1017/S0013091500010282 —, Quotients of F-spaces (to appear). —, The three space problem for locally bounded spaces (to appear). 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).
- M. Ribe, On the separation properties of the duals of general topological vector spaces, Ark. Mat. 9 (1971), 279–302. MR 324358, DOI 10.1007/BF02383651
- M. Ribe, Necessary convexity conditions for the Hahn-Banach theorem in metrizable spaces, Pacific J. Math. 44 (1973), 715–732. MR 324359
- 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) Lecture Notes in Math., Vol. 604, Springer, Berlin, 1977, pp. 76–81. MR 0625305
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 351-355
- MSC: Primary 46A10
- DOI: https://doi.org/10.1090/S0002-9939-1979-0518518-9
- MathSciNet review: 518518