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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  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 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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