# On sequential convergence in weakly compact subsets of Banach spaces

Studia Mathematica (1995)

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

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topMarciszewski, 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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- [Ne] S. Negrepontis, Banach spaces and topology, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 1045-1142.
- [Ny1] P. Nyikos, Classes of compact sequential spaces, in: Set Theory and its Applications, Lecture Notes in Math. 1401, Springer, 1989, 135-159.
- [Ny2] P. Nyikos, Properties of Eberlein compacta, Abstracts of Eighth Summer Conference on General Topology and Applications, 1992, 28.
- [Po] R. Pol, Note on pointwise convergence of sequences of analytic sets, Mathematika 36 (1989), 290-300. Zbl0719.54047

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