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Products of Lipschitz-free spaces and applications

Pedro Levit Kaufmann — 2015

Studia Mathematica

We show that, given a Banach space X, the Lipschitz-free space over X, denoted by ℱ(X), is isomorphic to ( n = 1 ( X ) ) . Some applications are presented, including a nonlinear version of Pełczyński’s decomposition method for Lipschitz-free spaces and the identification up to isomorphism between ℱ(ℝⁿ) and the Lipschitz-free space over any compact metric space which is locally bi-Lipschitz embeddable into ℝⁿ and which contains a subset that is Lipschitz equivalent to the unit ball of ℝⁿ. We also show that ℱ(M)...

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