Isometric embeddings of compact spaces into Banach spaces |
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Authors: | Y Dutrieux |
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Institution: | Université de Franche-Comté, Laboratoire de Mathématiques UMR 6623, 16 route de Gray, 25030 Besançon Cedex, France |
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Abstract: | We show the existence of a compact metric space K such that whenever K embeds isometrically into a Banach space Y, then any separable Banach space is linearly isometric to a subspace of Y. We also address the following related question: if a Banach space Y contains an isometric copy of the unit ball or of some special compact subset of a separable Banach space X, does it necessarily contain a subspace isometric to X? We answer positively this question when X is a polyhedral finite-dimensional space, c0 or ?1. |
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Keywords: | Isometric embeddings Compact metric spaces Geometry of Banach spaces |
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