The heredity problem for weakly compactly generated Banach spaces

Haskell P. Rosenthal

Compositio Mathematica (1974)

  • Volume: 28, Issue: 1, page 83-111
  • ISSN: 0010-437X

How to cite


Rosenthal, Haskell P.. "The heredity problem for weakly compactly generated Banach spaces." Compositio Mathematica 28.1 (1974): 83-111. <>.

author = {Rosenthal, Haskell P.},
journal = {Compositio Mathematica},
language = {eng},
number = {1},
pages = {83-111},
publisher = {Noordhoff International Publishing},
title = {The heredity problem for weakly compactly generated Banach spaces},
url = {},
volume = {28},
year = {1974},

AU - Rosenthal, Haskell P.
TI - The heredity problem for weakly compactly generated Banach spaces
JO - Compositio Mathematica
PY - 1974
PB - Noordhoff International Publishing
VL - 28
IS - 1
SP - 83
EP - 111
LA - eng
UR -
ER -


  1. [1] D. Amir and J. Lindenstrauss: The structure of weakly compact sets in Banach spaces. Ann. of Math.88 (1968) 35-46. Zbl0164.14903MR228983
  2. [2] H.H. Corson: The weak topology of a Banach space. Trans. Amer. Math. Soc., 101 (1961) 1-15. Zbl0104.08502MR132375
  3. [3] H.H. Corson and E. Michael: Metrizability of certain countable unions, Ill. J. Math.8 (1964) 351-360. Zbl0127.13203MR170324
  4. [4] W. Davis, T. Figiel, W. Johnson, and A. Pelozynski: Factoring weakly compact operators (to appear). Zbl0306.46020
  5. [5] N. Dunford and J.T. Schwartz: Linear Operators, Part I. New York, Interscience, 1958. Zbl0084.10402MR117523
  6. [6] D. Friedland: On closed subspaces of weakly compactly generated Banach spaces. Submitted to Israel J. Math. 
  7. [7] A. Grothendieck: Sur les applications linéaires faiblement compactes d'espaces du type C(K). Canad. J. Math., 5 (1953) 129-173. Zbl0050.10902MR58866
  8. [8] K. John and V. Zizler: Projections in dual weakly compactly generated Banach spaces (to appear) Studia Math. Zbl0247.46029MR336295
  9. [9] —: Smoothness and its equivalents in weakly compactly generated Banach spaces (to appear)J. Funct. Anal. Zbl0272.46012
  10. [10] M.I. Kadec and A. Pelczynski: Bases, lacunary sequences, and complemented subspaces in the spaces Lp. Studia Math.21 (1962) 161-176. Zbl0102.32202
  11. [11] J. Lindenstrauss: On a theorem of Murray and Mackey. Anais de Acad. Brasileira Cien.39 (1967) 1-6. Zbl0153.44201MR226366
  12. [12] —: Weakly compact sets - their topological properties and the Banach spaces they generate. Annals of Mathematics Studies69, Princeton Univ. Press (1972) 235-273. Zbl0232.46019
  13. [13] W. Johnson and J. Lindenstrauss: Some remarks on weakly compactly generated Banach spaces (to appear)Israel J. Math. Zbl0306.46021MR417760
  14. [14] H.P. Rosenthal: On injective Banach spaces and the spaces L∞(μ) for finite measures μ. Acta. Math.124 (1970) 205-248. Zbl0207.42803
  15. [15] —: On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from Lp(μ) to Lr(μ). J. Funct. Anal.2 (1969) 176-214. Zbl0185.20303
  16. [16] —: On relatively disjoint families of measures, with some applications to Banach space theory. Studia Math.37 (1970) 13-36. Zbl0227.46027
  17. [17] —: On the subspaces of Lp(p &gt; 2) spanned by independent random variables. Israel J. Math.8 (1970) 273-303. Zbl0213.19303
  18. [18] —: On the span in Lp of sequences of independent random variables (II). Berkeley Symposium on Mathematics, Statistics, and Probability, Vol. II (1972) 149-167. Zbl0255.60003
  19. [19] W. Sierpinski: Cardinal and Ordinal Numbers. Warsaw, Monografje Matematijczne, 1958. Zbl0083.26803MR95787
  20. [20] S.L. Troyanski: Equivalent norms and minimal systems in non-separable Banach spaces. Studia Math.43 (1972) 125-138. Zbl0255.46012MR324382

Citations in EuDML Documents

  1. Boris A. Efimov, G. I. Chertanov, О подпространствах Σ -приизведения отрезков
  2. M. Talagrand, Espaces de Banach faiblement k -analytiques
  3. David Preiss, Petr Simon, A weakly pseudocompact subspace of Banach space is weakly compact
  4. Genadij A. Sokolov, On some classes of compact spaces lying in Σ -products
  5. Petr Simon, On continuous images of Eberlein compacts
  6. Sophocles Mercourakis, E. Stamati, A new class of weakly K -analytic Banach spaces
  7. István Juhász, Zoltán Szentmiklóssy, Andrzej Szymański, Eberlein spaces of finite metrizability number
  8. W. Schachermayer, Eberlein-compacts et espaces de Radon
  9. Jiří Reif, Some remarks on subspaces of weakly compactly generated Banach spaces
  10. Aleksander V. Arhangel'skii, On bicompacta which are unions of two subspaces of a certain type

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.