Doré, Michael J. (2010) Universal Fréchet sets in Banach spaces. PhD thesis, University of Warwick.

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Abstract

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
Date:	March 2010
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Preiss, David
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC) EP/D053099/1 ; University of Warwick
Extent:	iv, 88 leaves
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/3688

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