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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The linear isometry group of the Gurarij space is universal


Author: Itaï Ben Yaacov
Journal: Proc. Amer. Math. Soc. 142 (2014), 2459-2467
MSC (2010): Primary 46B99, 22A05, 54D35
Published electronically: March 12, 2014
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11956-3
PII: S 0002-9939(2014)11956-3
Keywords: Gurarij space, Kat\v{e}tov function, Arens-Eells space, universal Polish group
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
Article copyright: © Copyright 2014 American Mathematical Society