Weak compactness criteria in symmetric spaces of measurable operators

The principal result of the paper reduces the study of certain weakly compact sets in Banach spaces of measurable operators to that of the corresponding sets of generalized singular value functions. In particular, under natural conditions, it is shown that the orbit of a relatively weakly compact subset of the Köthe dual of a symmetric space of measurable operators affiliated with some semi-finite von Neumann algebra is again relatively weakly compact.