# σ-fragmented Banach spaces II

J. Jayne; I. Namioka; C. Rogers

Studia Mathematica (1994)

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

## Access Full Article

top## Abstract

top## How to cite

topJayne, 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] D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. 88 (1968), 35-46. Zbl0164.14903
- [2] R. Deville, Problèmes de renormages, J. Funct. Anal. 68 (1986), 117-129. Zbl0607.46014
- [3] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Math. 64, Longman, Essex, 1993. Zbl0782.46019
- [4] R. Haydon, Some problems about scattered spaces, Séminaire Initiation à l'Analyse 9 (1989/90), 1-10.
- [5] R. Haydon, Trees in renorming theory, preprint. Zbl1036.46003
- [6] R. Haydon and C. A. Rogers, A locally uniformly convex renorming for certain C(K), Mathematika 37 (1990), 1-8. Zbl0725.46008
- [7] J. E. Jayne, I. Namioka and C. A. Rogers, Norm fragmented weak compact sets, Collect. Math. 41 (1990), 133-163. Zbl0764.46015
- [8] J. E. Jayne, I. Namioka and C. A. Rogers, σ-fragmented Banach spaces, Mathematika 39 (1992), 161-188 and 197-215.
- [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] J. E. Jayne, I. Namioka and C. A. Rogers, Fragmentability and σ-fragmentability, Fund. Math. 143 (1993), 207-220. Zbl0801.46011
- [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] 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] K. John and V. Zizler, Smoothness and its equivalents in weakly compactly generated Banach spaces, ibid. 15 (1974), 1-11. Zbl0272.46012
- [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] I. Namioka, Radon-Nikodým compact spaces and fragmentability, Mathematika 34 (1987), 258-281. Zbl0654.46017
- [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] N. K. Ribarska, Internal characterization of fragmentable spaces, Mathematika 34 (1987), 243-257. Zbl0645.46017
- [18] I. Singer, Bases in Banach Spaces II, Springer, Berlin, 1981.
- [19] V. Zizler, Locally uniformly rotund renorming and decomposition of Banach spaces, Bull. Austral. Math. Soc. 29 (1984), 259-265. Zbl0553.46014

## NotesEmbed ?

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