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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Coarse embeddings of metric spaces into Banach spaces
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by Piotr W. Nowak PDF
Proc. Amer. Math. Soc. 133 (2005), 2589-2596 Request permission

Abstract:

There are several characterizations of coarse embeddability of locally finite metric spaces into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces $L_p(\mu )$, we get their coarse embeddability into a Hilbert space for $0<p<2$. This together with a theorem by Banach and Mazur yields that coarse embeddability into $\ell _2$ and into $L_p(0,1)$ are equivalent when $1 \le p<2$. A theorem by G.Yu and the above allow us to extend to $L_p(\mu )$, $0<p\le 2$, the range of spaces, coarse embeddings into which is guaranteed for a finitely generated group $\Gamma$ to satisfy the Novikov Conjecture.
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Additional Information
  • Piotr W. Nowak
  • Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland – and – Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, Louisiana 70118
  • Address at time of publication: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240
  • Email: pnowak@math.vanderbilt.edu
  • Received by editor(s): October 5, 2003
  • Published electronically: April 19, 2005
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2005 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2589-2596
  • MSC (2000): Primary 46C05; Secondary 46T99
  • DOI: https://doi.org/10.1090/S0002-9939-05-08150-5
  • MathSciNet review: 2146202