(I)-envelopes of unit balls and James' characterization of reflexivity

Abstract

We study the (I)-envelopes of the unit balls of Banach spaces. We show, in particular, that any nonreflexive space can be renormed such that the (I)-envelope of the unit ball is not the whole bidual unit ball. Further, we give a simpler proof of the James' characterization of reflexivity in nonseparable case.

We also study the spaces in which the (I)-envelope of the unit ball adds nothing.

Keywords

• -envelopes
• balls
• James&apos
• characterization
• reflexivity