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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The quantum Gromov-Hausdorff propinquity
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by Frédéric Latrémolière PDF
Trans. Amer. Math. Soc. 368 (2016), 365-411 Request permission

Abstract:

We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel’s quantum Gromov-Hausdorff distance and Rieffel’s proximity by making *-isomorphism a necessary condition for distance zero, while being well adapted to Leibniz seminorms. This work offers a natural solution to the long-standing problem of finding a framework for the development of a theory of Leibniz Lip-norms over C*-algebras.
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Additional Information
  • Frédéric Latrémolière
  • Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
  • MR Author ID: 760927
  • Email: frederic@math.du.edu
  • Received by editor(s): November 6, 2013
  • Published electronically: May 22, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 365-411
  • MSC (2010): Primary 46L89, 46L30, 58B34
  • DOI: https://doi.org/10.1090/tran/6334
  • MathSciNet review: 3413867