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- W3024211597 abstract "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. Bru`e, 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 $p=1$." @default.
- W3024211597 created "2020-05-21" @default.
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- W3024211597 date "2021-07-15" @default.
- W3024211597 modified "2023-09-25" @default.
- W3024211597 title "Lipschitz free spaces isomorphic to their infinite sums and geometric applications" @default.
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- W3024211597 doi "https://doi.org/10.1090/tran/8444" @default.
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