COMPOSITION OPERATORS ON ANALYTIC VECTOR-VALUED NEVANLINNA CLASSES

摘要

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