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Let E be a Banach function space over a σ-finite measure space (Ω, Σ, μ), E'-the Kothe dual of E and let X be a reflexive Banach space, X * -the topological dual of X. We characterize relatively σ(E(X), E'(X * ))-compact subsets of a Kothe-Bochner space E(X) in terms of absolute continuity of certain seminorm defined on E'(X * ). As an application, we obtain that a solid subset...
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