Weakly compact composition operators on vector-valued BMOA (Q2484188)

If an analytic map \(\phi\) of the unit disc induces a compact composition operator \(C_\phi: f \to f \circ \phi\) on the space BMOA and \(X\) is a reflexive Banach space, then \(C_\phi\) is weakly compact on the vector-valued function space BMOA(X). To demonstrate that this main result of the article is independent from a known analogue for wBMOA(X) (a weak version of BMOA(X)) the authors prove that BMOA(X) does not form a closed subspace of wBMOA(X) for any infinite-dimensional Banach space \(X\).