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 \(\mathcal {N}\subset \mathcal {M},\) the canonical embedding of \(\mathcal {F}_p(\mathcal {N})\) into \(\mathcal {F}_p(\mathcal {M})\) is an isomorphism. The most significant result in this direction is that the answer is positive if \(\mathcal {N}\subset \mathcal {M}\) are metric spaces.