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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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The linear isometry group of the Gurarij space is universal
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by Itaï Ben Yaacov PDF
Proc. Amer. Math. Soc. 142 (2014), 2459-2467 Request permission

Abstract:

We give a construction of the Gurarij space analogous to Katětov’s construction of the Urysohn space. The adaptation of Katětov’s technique uses a generalisation of the Arens-Eells enveloping space to metric space with a distinguished normed subspace. This allows us to give a positive answer to a question of Uspenskij as to whether the linear isometry group of the Gurarij space is a universal Polish group.
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Additional Information
  • Itaï Ben Yaacov
  • Affiliation: Université Claude Bernard – Lyon 1, Institut Camille Jordan, CNRS UMR 5208, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
  • MR Author ID: 699648
  • Received by editor(s): June 27, 2012
  • Received by editor(s) in revised form: July 8, 2012, July 10, 2012, and July 31, 2012
  • Published electronically: March 12, 2014
  • Additional Notes: The author’s research was supported by the Institut Universitaire de France and ANR contract GruPoLoCo (ANR-11-JS01-008).
  • Communicated by: Thomas Schlumprecht
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2459-2467
  • MSC (2010): Primary 46B99, 22A05, 54D35
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11956-3
  • MathSciNet review: 3195767