On the approximation property for Banach spaces predual to H ∞-spaces ✩

A major open problem asks about the (Grothendieck) approximation property for the space H ∞ := H ∞ (D) of bounded holomorphic functions in the unit disk D ⊂ C. Motivated by this problem we establish approximation properties for Banach spaces predual to the spaces H ∞ (Ω) forΩ being finite direct products of starlike domains and unbranched coverings of strongly pseudoconvex domains in Stein manifolds. © 2012 Elsevier Inc. All rights reserved.