The Mazur-Ulam property for the space of complex null sequences
| Autor: | Jim��nez-Vargas, Antonio, Campoy, Antonio Morales, Peralta, Antonio M., Ram��rez, Mar��a Isabel |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Popis: | 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 $\ell_{\infty}^m$. |
| Databáze: | OpenAIRE |
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