COMPOSITION OPERATORS ON ANALYTIC VECTOR-VALUED NEVANLINNA CLASSES

Let ψ be an analytic self-map of the complex unit disk and X a Banach space.This paper studies the action of composition operator Cψ: f → fo ψ on the vector-valued Nevanlinna classes N(X) and Na(X). Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cψ is weakly compact on N(X) and Na(X) if and only if it is weakly compact on the vector-valued Hardy space H1 (X) and Bergman space B1 (X) respectively.

作 者： Wang Maofa   作者單位： Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China  刊 名： 數(shù)學(xué)物理學(xué)報(bào)（英文版）  ISTIC SCI 英文刊名： ACTA MATHEMATICA SCIENTIA  年，卷(期)： 2005 25(4)  分類號(hào)： O4  關(guān)鍵詞： Composition operator   boundedness   weak compactness   Carleson measure   vector-valued Nevanlinna class  

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