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On the equivalence between coarse and uniform embeddability of quasi-Banach spaces into a Hilbert space

Author: Michal Kraus
Journal: Proc. Amer. Math. Soc. 143 (2015), 4835-4844
MSC (2010): Primary 46B20; Secondary 51F99
Published electronically: April 13, 2015
MathSciNet review: 3391041
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Abstract: We give a direct proof of the fact that a quasi-Banach space coarsely embeds into a Hilbert space if and only if it uniformly embeds into a Hilbert space.

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Michal Kraus
Affiliation: Pohang Mathematics Institute, Pohang University of Science and Technology, San 31 Hyoja Dong, Nam-Gu, Pohang 790-784, Republic of Korea
Address at time of publication: Institute of Mathematics AS CR, Žitná 25, 115 67 Praha 1, Czech Republic

Keywords: Coarse embedding, uniform embedding, quasi-Banach space, Hilbert space
Received by editor(s): September 4, 2013
Received by editor(s) in revised form: September 8, 2014
Published electronically: April 13, 2015
Additional Notes: This work was supported by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Project No. 2012047640), and by the grants GAČR 201/11/0345 and PHC Barrande 2012-26516YG
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society

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