Abstract
If (›; §;„) is a flnite atomless measure space and X is a normed space, we prove that the space Lp(„;X), 1• p•1is a barrelled space of class@0, regardless of the barrelledness of X: That enables us to obtain a localization theorem of certain mappings deflned in Lp(„;X): By \space we mean a \real or complex Hausdorfi locally convex space. Given a dual pair (E;F), as usual ae(E;F) denotes the weak topology on E: If B is a subset of a linear space E,hBi will denote its linear hull.
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