The Dunford-Pettis property for certain planar uniform algebras (Q1822015)

A Banach space X has the Dunford Pettis property if whenever \(x_ n\to 0\) weakly and \(x^*_ n\to 0\) weakly (in \(X^*)\) the sequence \(<x^*_ n,x_ n>\to 0\). Using some ideas of J. Bourgain the authors show that T-invariant algebras have the D.P.P. This implies that the standard algebras A(K), R(K) and p(K), K compact in \({\mathbb{C}}\), have the D.P.P.