Fixed point properties in Hardy spaces (Q986567)

The author proves that \(H^1(\Delta)\) has the weak* fixed point property for left reversible semigroups, where \(\Delta \) denotes the open unit disc of \(\mathbb C\) and \[ H^p(\Delta)=\{f:\Delta \to\mathbb C\text{ holomorphic}:\|f\|_{H^p(\Delta)}<\infty\}, \] \(0<p\leq \infty\), is the Hardy space on \(\Delta\). Also, it is investigated the case of higher dimensions, the case of Hardy spaces on the polydisc, and then it is explained how the case of more general domains such as Euclidian balls can be treated with a similar approach.