Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673207 | Indagationes Mathematicae | 2008 | 20 Pages |
Abstract
Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X is defined as the space of the multipliers from X to Y. The space XY is a generalization of the classical Köthe dual space of X, which is obtained by taking Y = Lt(μ). Under minimal conditions, we can consider the Y-bidual space XYY of X (i.e. the Y-dual of XY). As in the classical case, the containment X ⊂ XYY always holds. We give conditions guaranteeing that X coincides with XYY, in which case X is said to be Y-perfect. We also study when X is isometrically embedded in XYY. Properties involving p-convexity, p-concavity and the order of X and Y, will have a special relevance.
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