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Factorization of Analytic Functions with Values in Non-Commutative L1-spaces and Applications

Published online by Cambridge University Press:  20 November 2018

Uffe Haagerup  and
Gilles Pisier
Uffe Haagerup
Affiliation:
Odense University, Odense, Denmark
Gilles Pisier
Affiliation:
Université Paris VI, Paris, France
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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 H1(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 H1-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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 5 , 01 October 1989 , pp. 882 - 906
Copyright
Copyright © Canadian Mathematical Society 1989

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