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Theses

Plongements des espaces métriques dans les espaces de Banach.

Abstract : The central theme of this thesis is the embedding of metric spaces into Banach spaces. The embeddings can be different in nature. In this work we mainly focus on coarse, uniform or Lipschitz embeddings. We consider questions about the Lipschitz embedding of various classes of metric spaces, namely locally finite metric spaces or more generally locally finite subsets of Lp-spaces, with 1<= p <= [infinite]. These questions are closely related with the Lipschitz classification of Banach spaces. The coarse embeddings are a key tool in the study of several famous conjectures (coarse Baum-Connes conjecture, coarse Novikov conjecture...). That's why we carefully study the coarse embedding, and the uniform embedding, of proper metric spaces into Banach spaces without cotype. Another vaste field of investigation is what Manor Mendel and Assaf Naor have called the “Ribe program”. Local properties of Banach spaces, i.e properties involving only a finite number of vectors, should have a purely metric characterization. For this aim we study the embedding of special trees.
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Submitted on : Thursday, April 29, 2010 - 10:05:23 AM
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  • HAL Id : tel-00477415, version 1

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Florent Baudier. Plongements des espaces métriques dans les espaces de Banach.. Mathématiques [math]. Université de Franche-Comté, 2009. Français. ⟨tel-00477415⟩

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