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arXiv · 1711.00262

Non-expansive bijections to the unit ball of $\ell_1$-sum of strictly convex Banach spaces

Vladimir Kadets·Olesia Zavarzina
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Abstract

Extending recent results by Cascales, Kadets, Orihuela and Wingler (2016), Kadets and Zavarzina (2017), and Zavarzina (2017) we demonstrate that for every Banach space $X$ and every collection $Z_i, i\in I$ of strictly convex Banach spaces every non-expansive bijection from the unit ball of $X$ to the unit ball of sum of $Z_i$ by $\ell_1$ is an isometry.

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Vladimir Kadets, Olesia Zavarzina. 2017-11-01. Non-expansive bijections to the unit ball of $\ell_1$-sum of strictly convex Banach spaces. https://arxiv.org/abs/1711.00262

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