Let be an ideal of over a -finite measure space , and let be a real Banach space. Let be a subspace of the space of -equivalence classes of all strongly -measurable functions and consisting of all those for which the scalar function belongs to . Let stand for the order continuous dual of . We examine the Mackey topology in case when it is locally solid. It is shown that is the finest Hausdorff locally convex-solid topology on with the Lebesgue property. We obtain that the space is complete and sequentially barreled whenever is perfect. As an application, we obtain the Hahn-Vitali-Saks type theorem for sequences in . In particular, we consider the Mackey topology on Orlicz-Bochner spaces . We show that the space is complete iff is perfect. Moreover, it is shown that the Mackey topology is a mixed topology.
Cite this article
Marian Nowak, Mackey Topologies on Vector-Valued Function Spaces. Z. Anal. Anwend. 24 (2005), no. 2, pp. 327–340DOI 10.4171/ZAA/1243