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Analytic functions with values in lattices and symmetric spaces of measurable operators

Published online by Cambridge University Press:  24 October 2008

Quanhua Xu
Quanhua Xu
Affiliation:
Université des Sciences et Techniques de Lille Flandres Artois, U.F.R. de Mathématiques Pures et Appliquées, U.R.A. C.N.R.S. D 751, 59655 Villeneuve d'ascq Cedex, France and Wuhan University
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Abstract

Let 0 < p,pi ≤ ∞, 0 < q,qi < ∞ (i = 1, 2) such that

Let E be a quasi-Banach lattice which fails to contain c0 and whose α-convexity constant is equal to 1 for some 0 < α < ∞. Then for every f∈H(E(q)) there exist g∈Hp, 0(E(q0)), h∈Hp1(E(q1)) such that

Consequently, E is q-concave for some finite q if and only if E is uniformly H1-convexifiable in the sense of [24]. Analogous results are also obtained for symmetric spaces of measurable operators. Another result proved in the paper says that if E is a symmetric quasi-Banach function space on (0, ∞) having the analytic Radon–Nikodym property then LE(M, τ) also possesses this property for any semifinite von Neumann algebra (M, τ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 3 , May 1991 , pp. 541 - 563
Copyright
Copyright © Cambridge Philosophical Society 1991

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