James’ Characterisation of Weak Compactness

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dc.contributor.advisor Moors, W en
dc.contributor.author White, Samuel en
dc.date.accessioned 2017-12-11T21:23:19Z en
dc.date.issued 2017 en
dc.identifier.uri http://hdl.handle.net/2292/36732 en
dc.description Full text is available to authenticated members of The University of Auckland only. en
dc.description.abstract This thesis gives a detailed account of James’ famous characterisation of weak compactness, originally from [15]. We give a full proof of James’ Theorem, and then prove a number of related problems using the same techniques. Firstly, we generalise James’ result to a statement about the subdifferential of a continuous, convex function. Then, we show how James’ original approach can be used to prove a result about the notion of (I)-generation from [23]. Lastly, we present results about how the topology of the set of all norm-attaining functionals characterises reflexivity. Our approach combines the work of James with the work of Jimenez Sevilla and Moreno from [17]. en
dc.publisher ResearchSpace@Auckland en
dc.relation.ispartof Masters Thesis - University of Auckland en
dc.relation.isreferencedby UoA99265083113702091 en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights Restricted Item. Available to authenticated members of The University of Auckland. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/nz/ en
dc.title James’ Characterisation of Weak Compactness en
dc.type Thesis en
thesis.degree.discipline Mathematics en
thesis.degree.grantor The University of Auckland en
thesis.degree.level Masters en
dc.rights.holder Copyright: The author en
pubs.elements-id 719059 en
pubs.record-created-at-source-date 2017-12-12 en

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