论文标题
Lipschitz自由空间的紧凑型降低
Compact reduction in Lipschitz free spaces
论文作者
论文摘要
我们证明了一个不含Lipschitz的空间的弱预修套装所满足的一般原则。通过这一原则，在一般度量空间上不含Lipschitz的空间中的某些无限尺寸现象可能会降低到其紧凑型子集上的自由空间中的相同现象。作为简单的后果，我们得出了几个新的和一些已知的结果。主要的新结果是：$ \ Mathcal f（x）$对于每个超级反射Banach Space $ X $均依次依次完成，而$ \ Mathcal f（m）$具有Schur属性和每个分散的完整公制$ M $的近似属性。
We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. The main new results are: $\mathcal F(X)$ is weakly sequentially complete for every superreflexive Banach space $X$, and $\mathcal F(M)$ has the Schur property and the approximation property for every scattered complete metric space $M$.
