Somayeh Ebrahimi - Organization of education and training, Khodabandeh branch, Zanjan, Iran

In this paper, first we study properties of weak topologies induced on Banach function spaces by certain subsets of their associate spaces. We characterise relative sequential compactness in the weak topology and prove that the notions of relative weak compactness and relative weak sequential compactness coincide. Finally we apply the results attained to linearoperators and their adjoints acting on Banach function spaces.

Banach function space, weak topology, weak compactness, weakly compactoperator, strong* topology