A vector-valued version of Grothendieck's inequality (which seems to be of independent interest) is used to show that for operators between operator spaces the completely bounded norm and the so-called (∞, 1)-completely bounded norm are equivalent - the latter norm is a priori larger than the cb-norm and the largest among the scale of all (q,p)-completely bounded norms (for q = p originally invented by Pisier). The link between these two Grothendieck type inqualities is a vector-valued version of the Maurey-Rosenthal factorization theorem.
|Original language||English (US)|
|Number of pages||16|
|Journal||Indiana University Mathematics Journal|
|State||Published - Mar 1 1999|
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