This is an announcement for the paper "The Schur l1 Theorem for filters" by Antonio Aviles, Bernardo Cascales, Vladimir Kadets, and Alexander Leonov.

Abstract: We study the classes of filters F on N such that the weak and strong F-convergence of sequences in l1 coincide. We study also an analogue of l1 weak sequential completeness theorem for filter convergence.

Archive classification: math.FA math.GN

Citation: Journal of Mathematical Physics, Analysis, Geometry: 2007, v. 3,

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http://front.math.ucdavis.edu/0903.0659

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http://arXiv.org/abs/0903.0659

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