Let X be a real Banach space that does not contain a copy of l1. Then X* contains asymptotically isometric copies of l1 if and only if X has a quotient which is asymptotically isometric to c0.
@article{urn:eudml:doc:44340, title = {Asymptotically isometric copies of c0 and l1 in quotients of Banach spaces.}, journal = {Collectanea Mathematica}, volume = {55}, year = {2004}, pages = {237-242}, zbl = {1068.46004}, mrnumber = {MR2099214}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44340} }
Dongyang, Chen. Asymptotically isometric copies of c0 and l1 in quotients of Banach spaces.. Collectanea Mathematica, Tome 55 (2004) pp. 237-242. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44340/