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Title: Bourgain's l1 index
Keywords: Banach Space Theory, Ordinal Indices
Issue Date: 4-May-2007
Citation: CHUNG YEONG CHYUAN (2007-05-04). Bourgain's l1 index. ScholarBank@NUS Repository.
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.
Appears in Collections:Master's Theses (Open)

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