Every non-smooth $2$-dimensional Banach space has the Mazur-Ulam property

Taras Banakh; Javier Cabello Sánchez

doi:10.1016/j.laa.2021.04.020

Every non-smooth $2$-dimensional Banach space has the Mazur-Ulam property

Functional Analysis 2021-11-01 v1 Metric Geometry

Authors: Taras Banakh , Javier Cabello Sánchez

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Abstract

A Banach space $X$ has the $Mazur$ - $Ulam$ $property$ if any isometry from the unit sphere of $X$ onto the unit sphere of any other Banach space $Y$ extends to a linear isometry of the Banach spaces $X,Y$ . A Banach space $X$ is called $smooth$ if the unit ball has a unique supporting functional at each point of the unit sphere. We prove that each non-smooth 2-dimensional Banach space has the Mazur-Ulam property.

Keywords

banach space mazur-ulam property isometry unit sphere smoothness two-dimensional

Cite

@article{arxiv.2103.09266,
  title  = {Every non-smooth $2$-dimensional Banach space has the Mazur-Ulam property},
  author = {Taras Banakh and Javier Cabello Sánchez},
  journal= {arXiv preprint arXiv:2103.09266},
  year   = {2021}
}

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13 pages

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