Jordan norms for multilinear maps on C∗-algebras and Grothendieck's inequalities
DOI:
https://doi.org/10.7146/math.scand.a-143520Abstract
There exists a generalization of the concept completely bounded norm, for multilinear maps on C∗-algebras. We will use the word Jordan norm, for this norm and denote it by ‖⋅‖J. The Jordan norm ‖Φ‖J of a multilinear map is obtained via factorizations of Φ in the form Φ(a1,…,an)=T0σ1(a1)T1⋯T(n−1)σn(an)Tn, where the maps σi are Jordan homomorphisms. We show that any bounded bilinear form on a pair of C∗-algebras is Jordan bounded and satisfies ‖B‖J≤2‖B‖.
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