Universal Fréchet sets in Banach spaces
Doré, Michael J. (2010) Universal Fréchet sets in Banach spaces. PhD thesis, University of Warwick.
WRAP_THESIS_Dore_2010.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://webcat.warwick.ac.uk/record=b2338614~S15
We define a universal Fréchet set S of a Banach space Y as a subset containing a point of Fréchet differentiability of every Lipschitz function g : Y -> R. We prove a sufficient condition for S to be a universal Fréchet set and use this to construct new examples of such sets. The strongest such result says that in a non-zero Banach space Y with separable dual one can find a universal Fréchet set S ⊆ Y that is closed, bounded and has Hausdorff dimension one.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Fréchet spaces, Banach spaces, Lipschitz spaces|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Sponsors:||Engineering and Physical Sciences Research Council (EPSRC) EP/D053099/1 ; University of Warwick|
|Extent:||iv, 88 leaves|
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