We relate the Grothendieck inequality to the theory of vector measures and show that the integral of an inner product with respect to a bimeasure can be computed in an iterative way. We then show an application to the theory of bounded linear operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-1-6, author = {Adam Bowers}, title = {Vector integration and the Grothendieck inequality}, journal = {Studia Mathematica}, volume = {196}, year = {2010}, pages = {85-103}, zbl = {1205.46024}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-1-6} }
Adam Bowers. Vector integration and the Grothendieck inequality. Studia Mathematica, Tome 196 (2010) pp. 85-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-1-6/