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.
@article{bwmeta1.element.bwnjournal-article-smv112i2p189bwm,
author = {Witold Marciszewski},
title = {On sequential convergence in weakly compact subsets of Banach spaces},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {189-194},
zbl = {0822.46004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv112i2p189bwm}
}
Marciszewski, Witold. On sequential convergence in weakly compact subsets of Banach spaces. Studia Mathematica, Tome 113 (1995) pp. 189-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv112i2p189bwm/
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