Some Operator Ideals in Non-Commutative Functional Analysis

We characterize classes of linear maps between operator spaces $E$, $F$ whichfactorize through maps arising in a natural manner via the Pisier vector-valuednon-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on theseparable Hilbert space $l^2$. These classes of maps can be viewed asquasi-normed operator ideals in the category of operator spaces, that is innon-commutative (quantized) functional analysis. The case $p=2$ provides aBanach operator ideal and allows us to characterize the split property forinclusions of $W^*$-algebras by the 2-factorable maps. The variouscharacterizations of the split property have interesting applications inQuantum Field Theory.