Some Operator Ideals in Non-Commutative Functional Analysis

  • F. Fidaleo

    Università di Roma Tor Vergata, Italy


We study classes of linear maps between operator spaces EE and FF which factorize through maps arising in a natural manner by the Pisier vector-valued non-commutative LpL^p-spaces Sp[E]S_p[E] based on the Schatten classes on the separable Hilbert space 2\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 WW*-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. 759–776

DOI 10.4171/ZAA/849