Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of and can be controlled by the Szlenk index of E, where the Szlenk index is an ordinal index associated with a separable Banach space which provides a transfinite measure of the separability of the dual space.
@article{bwmeta1.element.bwnjournal-article-fmv152i1p55bwm,
author = {Beno\^\i t Bossard},
title = {An ordinal version of some applications of the classical interpolation theorem},
journal = {Fundamenta Mathematicae},
volume = {154},
year = {1997},
pages = {55-74},
zbl = {0901.46011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv152i1p55bwm}
}
Bossard, Benoît. An ordinal version of some applications of the classical interpolation theorem. Fundamenta Mathematicae, Tome 154 (1997) pp. 55-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv152i1p55bwm/
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