Please use this identifier to cite or link to this item:
https://scholarbank.nus.edu.sg/handle/10635/16257
DC Field | Value | |
---|---|---|
dc.title | Bourgain's l1 index | |
dc.contributor.author | CHUNG YEONG CHYUAN | |
dc.date.accessioned | 2010-04-08T11:02:48Z | |
dc.date.available | 2010-04-08T11:02:48Z | |
dc.date.issued | 2007-05-04 | |
dc.identifier.citation | CHUNG YEONG CHYUAN (2007-05-04). Bourgain's l1 index. ScholarBank@NUS Repository. | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/16257 | |
dc.description.abstract | In the last few decades, there has been much interest in the use of ordinal indices in Banach space theory. In the thesis we survey some results concerning Bourgain's \ell_{1} Index which gives an indication of the complexity of \ell_{1}^{n}'s in a separable Banach space. We begin with a paper by J. Bourgain himself, where he related the Lavrentiev index of elements in the second dual of a separable Banach space (regarded as Baire-1 functions when restricted to the dual ball) to the order of some \ell_{1} tree. We will obtain an improvement of his result. Then we look at some of the work done by D. Alspach, R. Judd and E. Odell, where properties of the \ell_{1} index were investigated and the indices of some explicit spaces were computed. | |
dc.language.iso | en | |
dc.subject | Banach Space Theory, Ordinal Indices | |
dc.type | Thesis | |
dc.contributor.department | MATHEMATICS | |
dc.contributor.supervisor | LEUNG HO-HON, DENNY | |
dc.description.degree | Master's | |
dc.description.degreeconferred | MASTER OF SCIENCE | |
dc.identifier.isiut | NOT_IN_WOS | |
Appears in Collections: | Master's Theses (Open) |
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Bourgains l1 Index.pdf | 488.17 kB | Adobe PDF | OPEN | None | View/Download |
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