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

Studia Mathematica (1991)

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

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topFabian, 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

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- [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] S. Mercourakis, On weakly countably determined Banach spaces, Trans. Amer. Math. Soc. 300 (1987), 307-327. Zbl0621.46018
- [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] M. Talagrand, Espaces de Banach faiblement K-analytiques, Ann. of Math. 110 (1979), 407-438. Zbl0393.46019
- [10] S. Troyanski, On locally uniformly convex and differentiable norms in certain nonseparable Banach spaces, Studia Math. 37 (1971), 173-180. Zbl0214.12701
- [11] L. Vašák, On one generalization of weakly compactly generated Banach spaces, ibid. 70 (1981), 11-19. Zbl0376.46012

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