Publication at Faculty of Mathematics and Physics |
2007
Abstract
We study the notion of (I)-generating introduced by V. Fonf and J.
Lindendstrauss and a related notion of (I)-envelope. As a consequence of our results we get an easy proof of the James characterization of weak compactness in Banach spaces with weak* angelic dual unit ball and an easy proof of the James characterization of reflexivity within a large class of spaces.
We also show by an example that the general James theorem cannot be proved by this method.