Defense Date

2013

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematical Sciences

First Advisor

Kevin Beanland

Abstract

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.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

May 2013

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