Grothendieck's inequalities revisited
We review the main results, recently obtained by the authors,
on Grothendieck's inequalities for real and complex JB*-triples.
We prove some new related facts. Most novelties consist in getting
better values for the constants involved in Grothendieck's inequalities.
In some case such an improvement needs a completely new
proof. We also show that the conjectures established by Barton-Friedman
and Chu-Iochum-Loupias are valid (even for real JB*-triples) whenever
we allow a small enlargement of the family of prehilbert seminorms (| |_\varphi).
Antonio M. Peralta <aperalta@goliat.ugr.es>
Angel Rodríguez Palacios <apalacio@goliat.ugr.es;