Some Operator Ideals in Non-commutative Functional Analysis
نویسنده
چکیده
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 spaces Sp[E ∗] based on the Schatten classes on the separable Hilbert space l. These classes of maps can be viewed as quasi-normed operator ideals in the category of operator spaces, that is in noncommutative (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. Mathematics Subject Classification Numbers: Primary 47D15, 47D25, Secondary 46L35.
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