σ-fragmented Banach spaces II

J. Jayne; I. Namioka; C. Rogers

Studia Mathematica (1994)

  • Volume: 111, Issue: 1, page 69-80
  • ISSN: 0039-3223

Abstract

top
Recent papers have investigated the properties of σ-fragmented Banach spaces and have sought to find which Banach spaces are σ-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be σ-fragmented using weakly closed sets. Zizler has shown that Banach spaces satisfying certain conditions have locally uniformly convex norms. Banach spaces that satisfy similar, but weaker conditions are shown to be σ-fragmented. An example, due to R. Pol, is given of a Banach space that is σ-fragmented using differences of weakly closed sets, but is not σ-fragmented using weakly closed sets.

How to cite

top

Jayne, J., Namioka, I., and Rogers, C.. "σ-fragmented Banach spaces II." Studia Mathematica 111.1 (1994): 69-80. <http://eudml.org/doc/216120>.

@article{Jayne1994,
abstract = {Recent papers have investigated the properties of σ-fragmented Banach spaces and have sought to find which Banach spaces are σ-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be σ-fragmented using weakly closed sets. Zizler has shown that Banach spaces satisfying certain conditions have locally uniformly convex norms. Banach spaces that satisfy similar, but weaker conditions are shown to be σ-fragmented. An example, due to R. Pol, is given of a Banach space that is σ-fragmented using differences of weakly closed sets, but is not σ-fragmented using weakly closed sets.},
author = {Jayne, J., Namioka, I., Rogers, C.},
journal = {Studia Mathematica},
keywords = {-fragmented Banach spaces; norming -basis; locally uniformly convex norms},
language = {eng},
number = {1},
pages = {69-80},
title = {σ-fragmented Banach spaces II},
url = {http://eudml.org/doc/216120},
volume = {111},
year = {1994},
}

TY - JOUR
AU - Jayne, J.
AU - Namioka, I.
AU - Rogers, C.
TI - σ-fragmented Banach spaces II
JO - Studia Mathematica
PY - 1994
VL - 111
IS - 1
SP - 69
EP - 80
AB - Recent papers have investigated the properties of σ-fragmented Banach spaces and have sought to find which Banach spaces are σ-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be σ-fragmented using weakly closed sets. Zizler has shown that Banach spaces satisfying certain conditions have locally uniformly convex norms. Banach spaces that satisfy similar, but weaker conditions are shown to be σ-fragmented. An example, due to R. Pol, is given of a Banach space that is σ-fragmented using differences of weakly closed sets, but is not σ-fragmented using weakly closed sets.
LA - eng
KW - -fragmented Banach spaces; norming -basis; locally uniformly convex norms
UR - http://eudml.org/doc/216120
ER -

References

top
  1. [1] D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. 88 (1968), 35-46. Zbl0164.14903
  2. [2] R. Deville, Problèmes de renormages, J. Funct. Anal. 68 (1986), 117-129. Zbl0607.46014
  3. [3] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Math. 64, Longman, Essex, 1993. Zbl0782.46019
  4. [4] R. Haydon, Some problems about scattered spaces, Séminaire Initiation à l'Analyse 9 (1989/90), 1-10. 
  5. [5] R. Haydon, Trees in renorming theory, preprint. Zbl1036.46003
  6. [6] R. Haydon and C. A. Rogers, A locally uniformly convex renorming for certain C(K), Mathematika 37 (1990), 1-8. Zbl0725.46008
  7. [7] J. E. Jayne, I. Namioka and C. A. Rogers, Norm fragmented weak compact sets, Collect. Math. 41 (1990), 133-163. Zbl0764.46015
  8. [8] J. E. Jayne, I. Namioka and C. A. Rogers, σ-fragmented Banach spaces, Mathematika 39 (1992), 161-188 and 197-215. 
  9. [9] J. E. Jayne, I. Namioka and C. A. Rogers, Topological properties of Banach spaces, Proc. London Math. Soc. 66 (1993), 651-672. Zbl0793.54026
  10. [10] J. E. Jayne, I. Namioka and C. A. Rogers, Fragmentability and σ-fragmentability, Fund. Math. 143 (1993), 207-220. Zbl0801.46011
  11. [11] J. E. Jayne, I. Namioka and C. A. Rogers, Continuous functions on compact totally ordered spaces, J. Funct. Anal., to appear. Zbl0871.54022
  12. [12] J. E. Jayne, J. Orihuela, A. J. Pallarés and G. Vera, σ-fragmentability of multivalued maps and selection theorems, J. Funct. Anal. 117 (1993), 243-373. Zbl0822.54018
  13. [13] K. John and V. Zizler, Smoothness and its equivalents in weakly compactly generated Banach spaces, ibid. 15 (1974), 1-11. Zbl0272.46012
  14. [14] K. John and V. Zizler, Some remarks on non-separable Banach spaces with Markuševič basis, Comment. Math. Univ. Carolin. 15 (1974), 679-691. Zbl0291.46010
  15. [15] I. Namioka, Radon-Nikodým compact spaces and fragmentability, Mathematika 34 (1987), 258-281. Zbl0654.46017
  16. [16] I. Namioka and R. Pol, Mappings of Baire spaces into function spaces and Kadec renorming, Israel J. Math. 78 (1992), 1-20. Zbl0794.54036
  17. [17] N. K. Ribarska, Internal characterization of fragmentable spaces, Mathematika 34 (1987), 243-257. Zbl0645.46017
  18. [18] I. Singer, Bases in Banach Spaces II, Springer, Berlin, 1981. 
  19. [19] V. Zizler, Locally uniformly rotund renorming and decomposition of Banach spaces, Bull. Austral. Math. Soc. 29 (1984), 259-265. Zbl0553.46014

NotesEmbed ?

top

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.