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The three space problem for locally bounded F-spaces. (English) Zbl 0395.46003


MSC:

46A04 Locally convex Fréchet spaces and (DF)-spaces
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
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References:

[1] T. Aoki : Locally bounded linear topological spaces . Proc. Imp. Acad. Tokyo 18 (1942) No. 10. · Zbl 0060.26503 · doi:10.3792/pia/1195573733
[2] A. Beck : A convexity condition in Banach spaces and the strong law of large numbers . Proc. Amer. Math. Soc. 13 (1962) 329-334. · Zbl 0108.31401 · doi:10.2307/2034494
[3] S. Dierolf : Über Vererbbarkeitseigenschaften in topologischen Vektorräumen , Dissertation, Munich 1974.
[4] P. Enflo , J. Lindenstrauss and G. Pisier : On the ’three space problem’ . Math. Scand. 36 (1975) 199-210. · Zbl 0314.46015 · doi:10.7146/math.scand.a-11571
[5] D.P. Giesy : On a convexity condition in normed linear spaces . Trans. Amer. Math. Soc. 125 (1966) 114-146. · Zbl 0183.13204 · doi:10.2307/1994591
[6] N.J. Kalton : Orlicz sequence spaces without local convexity (to appear). · Zbl 0345.46013 · doi:10.1017/S0305004100053342
[7] N.J. Kalton and N.T. Peck : Quotients of Lp(0, 1) for 0 \leq p < 1 (to appear). · Zbl 0393.46007
[8] N.J. Kalton and J.H. Shapiro : Bases and basic sequences in F-spaces . Studia Math., 61 (1976) 47-61. · Zbl 0334.46008
[9] M. Ribe : l1 as a quotient space over an uncomplemented line (to appear).
[10] S. Rolewicz : On certain classes of linear metric spaces . Bull. Acad. Polon. Sci. 5 (1957) 471-473. · Zbl 0079.12602
[11] S. Rolewicz : Some remarks on the spaces N(L) and N(l) . Studia Math. 18 (1959) 1-9. · Zbl 0085.32301
[12] W.J. Stiles : Some properties of lp, 0 < p < 1 . Studia Math. 42 (1972) 109-119. · Zbl 0208.14502
[13] P. Turpin : Convexités dans les espaces vectoriels topologiques generaux , Diss. Math. No. 131, 1976. · Zbl 0331.46001
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