Factorization of Analytic Functions with Values in Non-Commutative L 1-spaces and Applications

Haagerup, Uffe ; Pisier, Gilles

Canadian journal of mathematics, Tome 41 (1989) no. 5, pp. 882-906

Résumé

Let X be a Banach space such that X* is a von Neumann algebra. We prove that X has the analytic Radon-Nikodym property (in short: ARNP). More precisely we show that for any function ƒ in H 1(X) we have This implies the ARNP for X as well as for all the Banach spaces which are finitely representable in X. The proof uses a C*-algebraic formulation of the classical factorization theorems for matrix valued H 1-functions. As a corollary we prove (for instance) that if A ⊂ B is a C*-subalgebra of a C*-algebra B, then every operator from A into H∞ extends to an operator from B into H∞ with the same norm. We include some remarks on the ARNP in connection with the complex interpolation method.

Détail

DOI : 10.4153/CJM-1989-041-6

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