Abstract
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.