On a dual locally uniformly rotund norm on a dual Vašák space

Marián Fabian

Studia Mathematica (1991)

  • Volume: 101, Issue: 1, page 69-81
  • ISSN: 0039-3223

Abstract

top
We transfer a renorming method of transfer, due to G. Godefroy, from weakly compactly generated Banach spaces to Vašák, i.e., weakly K-countably determined Banach spaces. Thus we obtain a new construction of a locally uniformly rotund norm on a Vašák space. A further cultivation of this method yields the new result that every dual Vašák space admits a dual locally uniformly rotund norm.

How to cite

top

Fabian, Marián. "On a dual locally uniformly rotund norm on a dual Vašák space." Studia Mathematica 101.1 (1991): 69-81. <http://eudml.org/doc/215893>.

@article{Fabian1991,
abstract = {We transfer a renorming method of transfer, due to G. Godefroy, from weakly compactly generated Banach spaces to Vašák, i.e., weakly K-countably determined Banach spaces. Thus we obtain a new construction of a locally uniformly rotund norm on a Vašák space. A further cultivation of this method yields the new result that every dual Vašák space admits a dual locally uniformly rotund norm.},
author = {Fabian, Marián},
journal = {Studia Mathematica},
keywords = {renorming method of transfer; weakly compactly generated Banach spaces; weakly -countably determined Banach spaces; locally uniformly rotund norm on a Vašák space},
language = {eng},
number = {1},
pages = {69-81},
title = {On a dual locally uniformly rotund norm on a dual Vašák space},
url = {http://eudml.org/doc/215893},
volume = {101},
year = {1991},
}

TY - JOUR
AU - Fabian, Marián
TI - On a dual locally uniformly rotund norm on a dual Vašák space
JO - Studia Mathematica
PY - 1991
VL - 101
IS - 1
SP - 69
EP - 81
AB - We transfer a renorming method of transfer, due to G. Godefroy, from weakly compactly generated Banach spaces to Vašák, i.e., weakly K-countably determined Banach spaces. Thus we obtain a new construction of a locally uniformly rotund norm on a Vašák space. A further cultivation of this method yields the new result that every dual Vašák space admits a dual locally uniformly rotund norm.
LA - eng
KW - renorming method of transfer; weakly compactly generated Banach spaces; weakly -countably determined Banach spaces; locally uniformly rotund norm on a Vašák space
UR - http://eudml.org/doc/215893
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] J. Diestel, Geometry of Banach Spaces, Selected Topics, Lecture Notes in Math. 485, Springer, Berlin 1975. Zbl0307.46009
  3. [3] N. Dunford and J. T. Schwartz, Linear Operators I, Interscience Publ., New York 1958. Zbl0084.10402
  4. [4] M. Fabian and S. Troyanski, A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space, Israel J. Math. 69 (1990), 214-224. Zbl0764.46012
  5. [5] G. Godefroy, Existence de normes très lisses sur certains espaces de Banach, Bull. Sci. Math. (2) 106 (1982), 63-68. Zbl0514.46012
  6. [6] G. Godefroy, S. Troyanski, J. Whitfield, and V. Zizler, Smoothness in weakly compactly generated Banach spaces, J. Funct. Anal. 52 (1983), 344-352. Zbl0517.46010
  7. [7] S. Mercourakis, On weakly countably determined Banach spaces, Trans. Amer. Math. Soc. 300 (1987), 307-327. Zbl0621.46018
  8. [8] S. Mercourakis, A dual weakly K-analytic Banach space is not necessarily a subspace of a weakly compactly generated Banach space, a manuscript. 
  9. [9] M. Talagrand, Espaces de Banach faiblement K-analytiques, Ann. of Math. 110 (1979), 407-438. Zbl0393.46019
  10. [10] S. Troyanski, On locally uniformly convex and differentiable norms in certain nonseparable Banach spaces, Studia Math. 37 (1971), 173-180. Zbl0214.12701
  11. [11] L. Vašák, On one generalization of weakly compactly generated Banach spaces, ibid. 70 (1981), 11-19. Zbl0376.46012

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.