We study the (I)-envelopes of the unit balls of Banach spaces. We show, in particular, that any nonreflexive space can be renormed in such a way that the (I)-envelope of the unit ball is not the whole bidual unit ball. Further, we give a simpler proof of James' characterization of reflexivity in the nonseparable case. We also study the spaces in which the (I)-envelope of the unit ball adds nothing.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-1-2,
author = {Ond\v rej F. K. Kalenda},
title = {(I)-envelopes of unit balls and James' characterization of reflexivity},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {29-40},
zbl = {1139.46018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-1-2}
}
Ondřej F. K. Kalenda. (I)-envelopes of unit balls and James' characterization of reflexivity. Studia Mathematica, Tome 178 (2007) pp. 29-40. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-1-2/