Weak compactness criteria in symmetric spaces of measurable operators

The principal result. of the paper reduces the study of certain weakly comp act sets in Banach spaces of measurable operators to that. of the correspon ding sets of generalized singular value functions. In particular, under nat ural conditions, it is shown that the orbit of a relatively weakly compact subset of the Kothe dual of a symmetric space of measurable operators affil iated with some semi-finite von Neumann algebra is again relatively weakly compact.