  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 $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the
separable Hilbert space $l^2$. 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.
