The goal of this thesis is to give an exposition of the following recent result of Freeman, Lennard, Odell, Turett and Randrianantoanina. A Banach space has the Schur property if and only if every weakly compact set is contained in the closed convex hull of a weakly null sequence. This result complements an old result of Grothendieck (now called the Grothendieck Compactness Principle) stating that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. We include many of the relevant definitions and preliminary results which are required in the proofs of both of these theorems.
Identifer | oai:union.ndltd.org:vcu.edu/oai:scholarscompass.vcu.edu:etd-4041 |
Date | 26 April 2013 |
Creators | Bjorkman, Kaitlin |
Publisher | VCU Scholars Compass |
Source Sets | Virginia Commonwealth University |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Theses and Dissertations |
Rights | © The Author |
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