The three space problem for locally bounded F -spaces

N. J. Kalton

Compositio Mathematica (1978)

  • Volume: 37, Issue: 3, page 243-276
  • ISSN: 0010-437X

How to cite


Kalton, N. J.. "The three space problem for locally bounded $F$-spaces." Compositio Mathematica 37.3 (1978): 243-276. <>.

author = {Kalton, N. J.},
journal = {Compositio Mathematica},
keywords = {Separating Dual; Locally Bounded F-Spaces; Three Space Problem; B-Convex Banach Spaces; R-Banach Space; Complemented Subspace},
language = {eng},
number = {3},
pages = {243-276},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {The three space problem for locally bounded $F$-spaces},
url = {},
volume = {37},
year = {1978},

AU - Kalton, N. J.
TI - The three space problem for locally bounded $F$-spaces
JO - Compositio Mathematica
PY - 1978
PB - Sijthoff et Noordhoff International Publishers
VL - 37
IS - 3
SP - 243
EP - 276
LA - eng
KW - Separating Dual; Locally Bounded F-Spaces; Three Space Problem; B-Convex Banach Spaces; R-Banach Space; Complemented Subspace
UR -
ER -


  1. [1] T. Aoki: Locally bounded linear topological spaces. Proc. Imp. Acad. Tokyo18 (1942) No. 10. Zbl0060.26503MR14182
  2. [2] A. Beck: A convexity condition in Banach spaces and the strong law of large numbers. Proc. Amer. Math. Soc.13 (1962) 329-334. Zbl0108.31401MR133857
  3. [3] S. Dierolf: Über Vererbbarkeitseigenschaften in topologischen Vektorräumen, Dissertation, Munich1974. 
  4. [4] P. Enflo, J. Lindenstrauss and G. Pisier: On the 'three space problem'. Math. Scand.36 (1975) 199-210. Zbl0314.46015MR383047
  5. [5] D.P. Giesy: On a convexity condition in normed linear spaces. Trans. Amer. Math. Soc.125 (1966) 114-146. Zbl0183.13204MR205031
  6. [6] N.J. Kalton: Orlicz sequence spaces without local convexity (to appear). Zbl0345.46013MR433194
  7. [7] N.J. Kalton and N.T. Peck: Quotients of Lp(0, 1) for 0 ≤ p &lt; 1 (to appear). Zbl0393.46007
  8. [8] N.J. Kalton and J.H. Shapiro: Bases and basic sequences in F-spaces. Studia Math., 61 (1976) 47-61. Zbl0334.46008MR420201
  9. [9] M. Ribe: l1 as a quotient space over an uncomplemented line (to appear). 
  10. [10] S. Rolewicz: On certain classes of linear metric spaces. Bull. Acad. Polon. Sci.5 (1957) 471-473. Zbl0079.12602MR88682
  11. [11] S. Rolewicz: Some remarks on the spaces N(L) and N(l). Studia Math.18 (1959) 1-9. Zbl0085.32301MR103413
  12. [12] W.J. Stiles: Some properties of lp, 0 &lt; p &lt; 1. Studia Math. 42 (1972) 109-119. Zbl0208.14502MR308726
  13. [13] P. Turpin: Convexités dans les espaces vectoriels topologiques generaux, Diss. Math. No. 131, 1976. Zbl0331.46001MR423044

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.