Extending surjective isometries defined on the unit sphere of $\ell_\infty(Γ)$

Antonio M. Peralta

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arXiv · 1709.09584

Extending surjective isometries defined on the unit sphere of $\ell_\infty(Γ)$

Antonio M. Peralta

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Abstract

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

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BibTeX RIS

Antonio M. Peralta. 2017-09-27. Extending surjective isometries defined on the unit sphere of $\ell_\infty(Γ)$. https://arxiv.org/abs/1709.09584

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