We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the -theorem by Rosenthal, it is proved that X contains order-one quasireflexive subspaces if X is not reflexive. Also, we obtain a characterization of the usual basis in .
@article{bwmeta1.element.bwnjournal-article-smv132i1p29bwm,
author = {Gin\'es L\'opez},
title = {Banach spaces with a supershrinking basis},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {29-36},
zbl = {0939.46011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv132i1p29bwm}
}
López, Ginés. Banach spaces with a supershrinking basis. Studia Mathematica, Tome 133 (1999) pp. 29-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv132i1p29bwm/
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