Some operator ideals in non-commutative functional analysis

We characterize classes of linear maps between operator spaces E, F which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative Lp spaces Sp[E∗] based on the Schatten classes on the separable Hilbert space l2. These classes of maps can be viewed as quasi-normed operator ideals in the category of operator spaces, that is in non-commutative (quantized) functional analysis. The case p=2 provides a Banach operator ideal and allows us to characterize the split property for inclusions of W∗-algebras by the 2-factorable maps. The various characterizations of the split property have interesting applications in Quantum Field Theory.