Let $M$ be a compact subset of a superreflexive Banach space. We prove thatthe Lipschitz-free space $\mathcal{F}(M)$, the predual of the Banach space ofLipschitz functions on $M$, has the Pe{\l}czy\'nski's property ($V^\ast$). As aconsequence, the Lipschitz-free space $\mathcal{F}(M)$ is weakly sequentiallycomplete.
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机译:令$ M $是超反射Banach空间的紧凑子集。我们证明无Lipschitz空间$ \ mathcal {F}(M)$(Lipschitz的Banach空间的前身在$ M $上起作用)具有Pe {\ l} czy \'nski的属性($ V ^ \ ast $ )。因此,无Lipschitz的空间$ \ mathcal {F}(M)$几乎没有顺序完成。
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