Some operator ideals in non-commutative functional analysis

Details Some operator ideals in non-commutative functional analysis Some operator ideals in non-commutative functional analysis

1997-09-26

arxiv.org/abs/funct-an/9709005v1

Mathematics

Operator Algebras

23 pages, LaTex

Scientific paper

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the separable Hilbert space $l^2$. These classes of maps can be viewed as quasi-normed operator ideals in the category of operator spaces, that is in non-commutative (quantized) functional analysis. The case $p=2$ provides a Banach operator ideal and allows us to characterize the split property for inclusions of $W^*$-algebras by the 2-factorable maps. The various characterizations of the split property have interesting applications in Quantum Field Theory.

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