This is an announcement for the paper “The Mazur-Ulam property for the space of complex null sequences” by Antonio Jiménez-Vargashttps://arxiv.org/find/math/1/au:+Jimenez_Vargas_A/0/1/0/all/0/1, Antonio Morales Campoyhttps://arxiv.org/find/math/1/au:+Campoy_A/0/1/0/all/0/1, Antonio M. Peraltahttps://arxiv.org/find/math/1/au:+Peralta_A/0/1/0/all/0/1, María Isabel Ramírezhttps://arxiv.org/find/math/1/au:+Ramirez_M/0/1/0/all/0/1.
Abstract: Given an infinite set $\Gamma$, we prove that the space of complex null sequences $c_0(\Gamma)$ satisfies the Mazur-Ulam property, that is, for each Banach space $X$, every surjective isometry from the unit sphere of $c_0(\Gamma)$ onto the unit sphere of $X$ admits a (unique) extension to a surjective real linear isometry from $c_0(\Gamma)$ to $X$. We also prove that the same conclusion holds for the finite dimensional space $\ell_{\infty}^m$.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.08538