Examples for the nonlocally convex three space problem
Author:
M. Ribe
Journal:
Proc. Amer. Math. Soc. 73 (1979), 351355
MSC:
Primary 46A10
MathSciNet review:
518518
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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 is locally convex.
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S. Dierolf, Über Vererbbarkeitseigenschaften in topologischen Vektorräumen, Dissertation, Munich 1974.
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M.
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topological vector spaces, Ark. Mat. 9 (1971),
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M.
Ribe, Necessary convexity conditions for the HahnBanach theorem in
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715–732. MR 0324359
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James
W. Roberts, A nonlocally convex 𝐹space with the
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604. MR
0625305 (58 #30008)
 [1]
 S. Dierolf, Über Vererbbarkeitseigenschaften in topologischen Vektorräumen, Dissertation, Munich 1974.
 [2]
 P. Enflo, J. Lindenstrauss and G. Pisier, On the ``three space problem", Math. Scand. 36 (1975), 199210. MR 0383047 (52:3928)
 [3]
 N. J. Kalton, Basic sequences in Fspaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151167. MR 0415259 (54:3350)
 [4]
 , Quotients of Fspaces (to appear).
 [5]
 , The three space problem for locally bounded spaces (to appear).
 [6]
 N. J. Kalton and N. T. Peck, Quotients of for , Notices Amer. Math. Soc. 24 (1977), p. A115; (to appear).
 [7]
 M. Ribe, On the separation properties of the duals of general topological vector spaces, Ark. Mat. 9 (1971), 279302. MR 0324358 (48:2710)
 [8]
 , Necessary convexity conditions for the HahnBanach theorem in metrizable spaces, Pacific J. Math. 44 (1973), 715732. MR 0324359 (48:2711)
 [9]
 J. Roberts, A nonlocally convex Fspace with the HahnBanach approximation property, Banach Spaces of Analytic Functions, Lecture Notes in Math., vol. 604, SpringerVerlag, Berlin, 1977, pp. 7681. MR 0625305 (58:30008)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197905185189
PII:
S 00029939(1979)05185189
Keywords:
Locally bounded space,
quotient space,
three space problem,
dualseparation
Article copyright:
© Copyright 1979 American Mathematical Society
