论文标题
Lipschitz代数和Lipschitz的空间在无限的度量空间上
Lipschitz algebras and Lipschitz-free spaces over unbounded metric spaces
论文作者
论文摘要
我们提出了一种将任意（无限制的）度量空间$ \ MATHCAL {M} $转入有限的度量空间$ \ Mathcal {B} $的方法，以使得相应的无lipschitz-fripschitz-fripsChitz-fripsChitz-fripsChitz-fripsChitz-fripsChitz-fripschitz-fripschitz-fripschitz-fripsCal $ \ Mathcal {f}（f}（\ Mathcal {m}）$ and $ \ Mathcal $ artcal $ artcal {f}同构。我们提供的构造在薄弱的意义上起作用，并且具有明确的优势。除了其内在的理论兴趣外，它还具有许多应用程序，因为它允许将许多对Lipschitz的空间有效的参数传输到有限的空间上，并在无界空间上传递到无lipschitz的空间。此外，我们表明，通过稍微修改的点乘法，标量 - 值lipschitz的Space $ \ rm {lip} _0（\ Mathcal {m}）$的lipschitz函数在任何（未绑定的）指数的Metric Space上在零（零）上消失了，它是Banach Algebra，它是Banach Algebra，它的banach Algebra具有其Canonical Lipschitz NormChitz Norm。
We present a way to turn an arbitrary (unbounded) metric space $\mathcal{M}$ into a bounded metric space $\mathcal{B}$ in such a way that the corresponding Lipschitz-free spaces $\mathcal{F}(\mathcal{M})$ and $\mathcal{F}(\mathcal{B})$ are isomorphic. The construction we provide is functorial in a weak sense and has the advantage of being explicit. Apart from its intrinsic theoretical interest, it has many applications in that it allows to transfer many arguments valid for Lipschitz-free spaces over bounded spaces to Lipschitz-free spaces over unbounded spaces. Furthermore, we show that with a slightly modified point-wise multiplication, the space $\rm{Lip}_0(\mathcal{M})$ of scalar-valued Lipschitz functions vanishing at zero over any (unbounded) pointed metric space is a Banach algebra with its canonical Lipschitz norm.
