The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (1179 KB) | Metadata | Table of Contents | ZAA summary
Volume 17, Issue 3, 1998, pp. 759–776
DOI: 10.4171/ZAA/849

Published online: 1998-09-30

Some Operator Ideals in Non-Commutative Functional Analysis

F. Fidaleo[1]

(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 [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.

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