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A weak Grothendieck compactness principle |
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| Authors: | PN Dowling D Freeman CJ Lennard E Odell B Randrianantoanina B Turett |
| Institution: | 1. Department of Mathematics, Miami University, Oxford, OH 45056, United States;2. Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, United States;3. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States;4. Department of Mathematics, Oakland University, Rochester, MI 48309, United States |
| Abstract: | The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In this article, an analogue of the Grothendieck compactness principle is considered when the norm topology of a Banach space is replaced by its weak topology. It is shown that every weakly compact subset of a Banach space is contained in the closed convex hull of a weakly null sequence if and only if the Banach space has the Schur property. |
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