(I)-envelopes of unit balls and James' characterization of reflexivity
Volume 182 / 2007
Studia Mathematica 182 (2007), 29-40
MSC: Primary 46B26; Secondary 46A55, 46B10.
DOI: 10.4064/sm182-1-2
Abstract
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.
