Duality theory of vector-valued function spaces. II. (English) Zbl 0908.46024
Summary: The paper is a continuation of part I [ibid. 37, 195-215 (1997; review above)], where the duality theory of Banach-space valued function spaces \(E(X)\) is developed. The notion of perfectness of the spaces \(E(X)\) is considered. It is proved that the space \(E(X)\) is perfect iff \(E\) is a perfect function space and the Banach space \(X\) is reflexive. Locally solid topologies on dual spaces of \(E(X)\) are considered. In particular, absolute weak topologies on duals of \(E(X)\) are examined.
MSC:
| 46E40 | Spaces of vector- and operator-valued functions |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 46A20 | Duality theory for topological vector spaces |
| 46A40 | Ordered topological linear spaces, vector lattices |
| 46B40 | Ordered normed spaces |
