ArticleOriginal scientific text
Title
Duality and some topological properties of vector-valued function spaces
Authors
Abstract
Let be an ideal of over -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 be equipped with a Hausdorff locally convex-solid topology and let stand for the topology on associated with . We examine the relationship between the properties of the space and the properties of both the spaces and . In particular, it is proved that (embedded in a natural way) is an order closed ideal of its bidual iff is an order closed ideal of its bidual and is reflexive. As an application, we obtain that is perfect iff is perfect and is reflexive.
Keywords
vector-valued function spaces, locally solid topologies, KB-spaces, Levy topologies, Lebesgue topologies, order dual, order continuous dual, perfectness