论文标题
Lipschitz的无限空间同构无限和几何应用
Lipschitz free spaces isomorphic to their infinite sums and geometric applications
论文作者
论文摘要
我们发现，在公制空间上不含Lipschitz的空间与其无限直接直接$ \ ell_1 $ sum同构并展示了几种应用。作为此类应用的示例，我们有同一有限维度的球和球的无lipschitz空间是同构的，即在$ \ mathbb {z}^d $上无lipschitz的空间与$ \ ell_1 $ - snowflake in snowflake and snowflake and snowflake and snowflake and snowflake and so的空间是同构的。 $ \ ell_1 $。此外，遵循[E. Bruè, S. Di Marino and F. Stra, Linear Lipschitz and $C^1$ extension operators through random projection, arXiv:1801.07533] we provide an elementary self-contained proof that Lipschitz-free spaces over doubling metric spaces are complemented in Lipschitz-free spaces over their superspaces and they have BAP.在更全面的$ p $ -banach空间的环境中探索了所有内容，包括有关倍增度空间的结果，这使我们能够欣赏案例之间理论的相似性和差异。
We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct $\ell_1$-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free spaces over balls and spheres of the same finite dimensions are isomorphic, that the Lipschitz-free space over $\mathbb{Z}^d$ is isomorphic to its $\ell_1$-sum, or that the Lipschitz-free space over any snowflake of a doubling metric space is isomorphic to $\ell_1$. Moreover, following new ideas from [E. Bruè, S. Di Marino and F. Stra, Linear Lipschitz and $C^1$ extension operators through random projection, arXiv:1801.07533] we provide an elementary self-contained proof that Lipschitz-free spaces over doubling metric spaces are complemented in Lipschitz-free spaces over their superspaces and they have BAP. Everything, including the results about doubling metric spaces, is explored in the more comprehensive setting of $p$-Banach spaces, which allows us to appreciate the similarities and differences of the theory between the cases $p<1$ and $p=1$.
