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Distortion of Lipschitz functions on $ c_0(\Gamma)$


Authors: Petr Hájek and Matěj Novotný
Journal: Proc. Amer. Math. Soc. 146 (2018), 2173-2180
MSC (2010): Primary 46B20, 46T20
DOI: https://doi.org/10.1090/proc/13945
Published electronically: January 8, 2018
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Abstract: Let $ \Gamma $ be an uncountable cardinal. We construct a real symmetric $ 1$-Lipschitz function on the unit sphere of $ c_0(\Gamma )$ whose restriction to any nonseparable subspace is a distortion.


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Petr Hájek
Affiliation: Mathematical Institute, Czech Academy of Science, Žitná 25, 115 67 Praha 1, Czech Republic – and – Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Jugoslávských partyzánů 3 166 27 Prague, Czech Republic
Email: hajek@math.cas.cz

Matěj Novotný
Affiliation: Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Jugoslávských partyzánů 3 166 27 Prague, Czech Republic
Email: novotny@math.feld.cvut.cz

DOI: https://doi.org/10.1090/proc/13945
Received by editor(s): April 29, 2017
Received by editor(s) in revised form: June 15, 2017, and August 9, 2017
Published electronically: January 8, 2018
Additional Notes: This work was supported in part by GAČR 16-07378S, RVO: 67985840 and by grant SGS15/194/OHK3/3T/13 of CTU in Prague.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2018 American Mathematical Society

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