We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson: "If a normed space E does not contain any asymptotically isometric copy of l1, then every bounded sequence of E' has a normalized l1-block sequence pointwise converging to 0".
@article{urn:eudml:doc:41841, title = {A new proof of James' sup theorem.}, journal = {Extracta Mathematicae}, volume = {20}, year = {2005}, pages = {261-271}, zbl = {1121.46013}, mrnumber = {MR2243342}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41841} }
Morillon, Marianne. A new proof of James' sup theorem.. Extracta Mathematicae, Tome 20 (2005) pp. 261-271. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41841/