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https://knowledgecommons.lakeheadu.ca/handle/2453/149
Title: | A Subspace of l2(X) without the approximation property |
Authors: | Chlebovec, Christopher |
Keywords: | Mathematics;Banach algebras |
Issue Date: | 10-Nov-2012 |
Abstract: | The aim of the thesis is to provide support to the following conjecture, which would provide an isomorphic characterization of a Hilbert space in terms of the approximation property: an infinite dimensional Banach space X is isomorphic to l₂ if and only if every subspace of l₂ (X) has the approximation property. We show that if X has cotype 2 and the sequence of Euclidean distances {dn(X *)}n of X * satisfies dn (X *) ≥ α(log2 n )β for all n ≥ 1 and some absolute constants α > 0 and β > 4, then [cursive l] 2 (X ) contains a subspace without the approximation property. |
URI: | http://knowledgecommons.lakeheadu.ca/handle/2453/149 |
metadata.etd.degree.discipline: | Mathematical Sciences |
metadata.etd.degree.name: | M.Sc. |
metadata.etd.degree.level: | Master |
metadata.dc.contributor.advisor: | Anisca, Razvan |
Appears in Collections: | Electronic Theses and Dissertations from 2009 |
Files in This Item:
File | Description | Size | Format | |
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ChleboverC2011m-1b.pdf | PDF/A - 1b compliance | 327.04 kB | Adobe PDF | ![]() View/Open |
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