This is an announcement for the paper “Extending surjective isometries defined on the unit sphere of $\ell_{\infty}(\Gamma)$” by Antonio M. Peraltahttps://arxiv.org/find/math/1/au:+Peralta_A/0/1/0/all/0/1.

Abstract: Let $\Gamma$ be an infinite set equipped with the discrete topology. We prove that the space $\ell_{\infty}(\Gamma)$, of all complex-valued bounded functions on $\Gamma$, satisfies the Mazur-Ulam property, that is, every surjective isometry from the unit sphere of $\ell_{\infty}(\Gamma)$ onto the unit sphere of an arbitrary complex Banach space X admits a unique extension to a surjective real linear isometry from $\ell_{\infty}(\Gamma)$ to $X$.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.09584