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 Spβ[Eβ] 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 Wβ-algebras by the 2-factorable maps. The various
characterizations of the split property have interesting applications in
Quantum Field Theory.Comment: 23 pages, LaTe