A result on the existence of global attractors for semigroups of closed operators

Abstract

In this note, we establish a general result on the existence of global attractorsfor semigroups $S(t)$ of operators acting on a Banach space $\mathcal X$, where the strongcontinuity $S(t)\in C(\mathcal X,\mathcal X)$ is replaced by the much weaker requirement that$S(t)$ be a closed map.