Quasi-isometries in continuous functions spaces

Vestfrid, Igor

doi:10.1090/proc/16570

Quasi-isometries in continuous functions spaces
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by Igor A. Vestfrid;

Proc. Amer. Math. Soc. 152 (2024), 739-748

DOI: https://doi.org/10.1090/proc/16570

Published electronically: November 21, 2023

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Abstract:

We consider quasi-isometries in real continuous functions spaces and show that such a quasi-isometry can be well approximated by an affine surjective isometry.

On the other hand, we give an example of quasi-isometries of the unit ball $B_H$ in a Hilbert space $H$ that are far from any affine map of $H$ and from any isometry of $B_H$.

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