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  • Author or Editor: Yunyan Yang x
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The concept of absolute convergence for series is generalized to locally convex spaces and an invariant theorem for absolutely convergent series in duality is established: when a locally convex space X is weakly sequentially complete, an admissible topology which is strictly stronger than the weak topology on X in the dual pair ( X,X′ ) is given such that it has the same absolutely convergent series as the weak topology in X .

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The key point of subseries convergence is discovered and the strongest Orlicz-Pettis-type result is established.

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