We study classes of linear maps between operator spaces and which factorize through maps arising in a natural manner by the Pisier vector-valued non-commutative -spaces based on the Schatten classes on the separable Hilbert space . These classes of maps, firstly introduced in  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 -algebras such as those describing the physical observables in Quantum Field Theory.
Cite this article
F. Fidaleo, Some Operator Ideals in Non-Commutative Functional Analysis. Z. Anal. Anwend. 17 (1998), no. 3, pp. 759–776DOI 10.4171/ZAA/849