Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1998-09-30
Some Operator Ideals in Non-Commutative Functional AnalysisF. Fidaleo (1) Università di Roma Tor Vergata, Italy
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  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.
Keywords: Linear spaces of operators; Operator algebras and ideals on Hubert spaces; Classifications, factors
Fidaleo F.: Some Operator Ideals in Non-Commutative Functional Analysis. Z. Anal. Anwend. 17 (1998), 759-776. doi: 10.4171/ZAA/849