Grothendieck's inequalities for real and complex JBW*-triples

In this paper we obtain Grothendieck's inequalities for real and complex JBW*-triples. We obtain these inequalities through results of C-H. Chu, B. Iochum, and G. Loupias, and a corrected version of the ``Little Grothendieck's inequality'' for complex JB*-triples due to T. Barton and Y. Friedman.
Antonio M. Peralta <aperalta@goliat.ugr.es> Angel Rodríguez Palacios <apalacio@goliat.ugr.es>