Canonical embedding of Lipschitz-free $p$-spaces

Abstract

We find a new finite algorithm for evaluation of Lipschitz-free $p$-space norm in finite-dimensional Lipschitz-free $p$-spaces. We use this algorithm to deal with the problem of whether given $p$-metric spaces $N\subset M$, the canonical embedding of ${\mathcal{F}}_p(N)$ into ${\mathcal{F}}_p(M)$ is an isomorphism. The most significant result in this direction is that the answer is positive if $N\subset M$ are metric spaces.

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