On sequential convergence in weakly compact subsets of Banach spaces

Witold Marciszewski

Studia Mathematica (1995)

  • Volume: 112, Issue: 2, page 189-194
  • ISSN: 0039-3223

Abstract

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We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.

How to cite

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Marciszewski, Witold. "On sequential convergence in weakly compact subsets of Banach spaces." Studia Mathematica 112.2 (1995): 189-194. <http://eudml.org/doc/216145>.

@article{Marciszewski1995,
abstract = {We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.},
author = {Marciszewski, Witold},
journal = {Studia Mathematica},
keywords = {Banach space; weakly compact set; uniform Eberlein compact space; bisequential space; weakly compact},
language = {eng},
number = {2},
pages = {189-194},
title = {On sequential convergence in weakly compact subsets of Banach spaces},
url = {http://eudml.org/doc/216145},
volume = {112},
year = {1995},
}

TY - JOUR
AU - Marciszewski, Witold
TI - On sequential convergence in weakly compact subsets of Banach spaces
JO - Studia Mathematica
PY - 1995
VL - 112
IS - 2
SP - 189
EP - 194
AB - We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.
LA - eng
KW - Banach space; weakly compact set; uniform Eberlein compact space; bisequential space; weakly compact
UR - http://eudml.org/doc/216145
ER -

References

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  1. [AF] S. Argyros and V. Farmaki, On the structure of weakly compact subsets of Hilbert spaces and applications to the geometry of Banach spaces, Trans. Amer. Math. Soc. 289 (1985), 409-427. Zbl0585.46010
  2. [BFT] J. Bourgain, D. H. Fremlin and M. Talagrand, Pointwise compact sets of Baire-measurable functions, Amer. J. Math. 100 (1978), 845-886. Zbl0413.54016
  3. [DFJP] W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327. Zbl0306.46020
  4. [Go] G. Godefroy, Compacts de Rosenthal, Pacific J. Math. 91 (1980), 293-306. 
  5. [LS] A. G. Leiderman and G. A. Sokolov, Adequate families of sets and Corson compacts, Comment. Math. Univ. Carolin. 25 (1984), 233-245. Zbl0586.54022
  6. [Ma] W. Marciszewski, On a classification of pointwise compact sets of the first Baire class functions, Fund. Math. 133 (1989), 195-209. Zbl0719.54022
  7. [Mi] E. Michael, A quintuple quotient test, Gen. Topology Appl. 2 (1972), 91-138. Zbl0238.54009
  8. [Ne] S. Negrepontis, Banach spaces and topology, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 1045-1142. 
  9. [Ny1] P. Nyikos, Classes of compact sequential spaces, in: Set Theory and its Applications, Lecture Notes in Math. 1401, Springer, 1989, 135-159. 
  10. [Ny2] P. Nyikos, Properties of Eberlein compacta, Abstracts of Eighth Summer Conference on General Topology and Applications, 1992, 28. 
  11. [Po] R. Pol, Note on pointwise convergence of sequences of analytic sets, Mathematika 36 (1989), 290-300. Zbl0719.54047

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