Abstract
We study classes of linear maps between operator spaces E and F which factorize through maps arising in a natural manner by the Pisier vector-valued non-commutative L^p -spaces S_p[E] based on the Schatten classes on the separable Hilbert space \ell ^2 . These classes of maps, firstly introduced in [28] and called p-nuclear maps, can be viewed as Banach operator ideals in the category of operator spaces, that is in non-commutative (quantized) functional analysis. We also discuss some applications to the split property for inclusions of W* -algebras such as those describing the physical observables in Quantum Field Theory.
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