Weakly compact composition operators on vector-valued BMOA

Weak compactness of the analytic composition operator f↦f○φ is studied on BMOA(X), the space of X-valued analytic functions of bounded mean oscillation, and its subspace VMOA(X), where X is a complex Banach space. It is shown that the composition operator is weakly compact on BMOA(X) if X is reflexive and the corresponding composition operator is compact on the scalar-valued BMOA. A concrete example is given which shows that BMOA(X) differs from the weak vector-valued BMOA for infinite dimensional Banach spaces X.