We characterise the Banach spaces X which are $L_1$-predual as those for which every Lipschitz compact mapping $f:N⟶X$ admits, for every $\epsilon >0$ and every M containing N, a Lipschitz (compact) extension $F:M⟶X$ so that $\Vert F\Vert \le (1+\epsilon )\Vert f\Vert$. Some consequences are derived about $L_1$-preduals and about Lipschitz-free spaces.

中文翻译：

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L1-preduals 在扩展 Lipschitz 映射方面的表征

我们刻画了 Banach 空间X，它们是${升}_1$-predual 就像每个 Lipschitz 紧凑映射的那些 $F：N⟶X$ 承认，对于每 $\epsilon >0$和每个包含N 的M，一个 Lipschitz（紧凑）扩展$F：米⟶X$ 以便 $\Vert F\Vert \le (1+\epsilon )\Vert F\Vert$. 一些后果是关于${升}_1$-preduals 和关于 Lipschitz-free 空间。