Into a Hilbert Space
نویسنده
چکیده
Nowak [N], improving a theorem due to A. N. Dranishnikov, G. Gong, V. Lafforgue, and G. Yu [DGLY], gave a characterization of coarse embeddability of general metric spaces into a Hilbert space using a result of Schoenberg on negative definite kernels. He used this characterization to show that the spaces Lp(μ) coarsely embed into a Hilbert space for p < 2. In this article, we show that lp does not coarsely embed into a Hilbert space when p > 2. It was already proved in [DGLY] that the Lipschitz universal space c0 (see [A]) does not coarsely embed into a Hilbert space. In its full generality, the statement of our result is as follows:
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