A Vector-Valued Grothendieck Inequality with an Application to (p,q)-Completely Bounded Operators

Andreas Defant, Marius Junge

Research output: Contribution to journalArticlepeer-review

Abstract

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 languageEnglish (US)
Pages (from-to)295-310
Number of pages16
JournalIndiana University Mathematics Journal
Volume48
Issue number1
StatePublished - Mar 1 1999
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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