Dual renormings of Banach spaces

Petr Hájek

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 241-253
  • ISSN: 0010-2628

Abstract

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We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.

How to cite

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Hájek, Petr. "Dual renormings of Banach spaces." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 241-253. <http://eudml.org/doc/247910>.

@article{Hájek1996,
abstract = {We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.},
author = {Hájek, Petr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Asplund space; weakly uniformly rotund norms; James spaces; equivalent WUR norm; Asplund space; dual renormings},
language = {eng},
number = {2},
pages = {241-253},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Dual renormings of Banach spaces},
url = {http://eudml.org/doc/247910},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Hájek, Petr
TI - Dual renormings of Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 241
EP - 253
AB - We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.
LA - eng
KW - Asplund space; weakly uniformly rotund norms; James spaces; equivalent WUR norm; Asplund space; dual renormings
UR - http://eudml.org/doc/247910
ER -

References

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  1. Deville R., Godefroy G., Zizler V., Smoothness and Renormings in Banach Spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64 (1993). Zbl0782.46019MR1211634
  2. Diestel J., Geometry of Banach Spaces-Selected Topics, Lecture Notes 485, SpringerVerlag, 1975. Zbl0466.46021MR0461094
  3. Hagler J., A counterexample to several questions about Banach spaces, Studia Math. 60 (1977), 289-308. (1977) Zbl0387.46015MR0442651
  4. James R.C., A non-reflexive Banach space isometric with its second conjugate, Proc. Nat. Acad. Sci. USA 37 (1951), 174-177. (1951) MR0044024
  5. James R.C., A separable somewhat reflexive space with nonseparable dual, Bull. Amer. Math. Soc. 80 (1974), 738-743. (1974) MR0417763
  6. Lindenstrauss J., Stegall C., Examples of separable spaces which do not contain ℓ 1 and whose duals are non-separable, Studia Math. 54 (1975), 81-105. (1975) Zbl0324.46017MR0390720
  7. Lindenstrauss J., Tzafriri L., Classical Banach Spaces I, Sequence Spaces, Springer-Verlag, 1977. Zbl0362.46013MR0500056
  8. Pelczynski A., On Banach spaces containing L 1 ( μ ) , Studia Math. 30 (1968), 231-246. (1968) MR0232195
  9. Singer I., On the problem of non-smoothness of non-reflexive second conjugate spaces, Bull. Austral. Math. Soc. 12 (1975), 407-416. (1975) Zbl0299.46017MR0383049
  10. Stegall C., The Radon-Nikodym property in conjugate Banach spaces, ibid. 206 (1975), 213-223. (1975) Zbl0318.46056MR0374381

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