Products of Lipschitz-free spaces and applications

• Autorzy: Pedro Levit Kaufmann
• Języki publikacji: EN

Abstrakty

EN

We show that, given a Banach space X, the Lipschitz-free space over X, denoted by ℱ(X), is isomorphic to $(∑_{n=1}^{∞}ℱ(X))_{ℓ₁}$. 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) is isomorphic to ℱ(c₀) for all separable metric spaces M which are absolute Lipschitz retracts and contain a subset which is Lipschitz equivalent to the unit ball of c₀. This class includes all C(K) spaces with K infinite compact metric (Dutrieux and Ferenczi (2006) already proved that ℱ(C(K)) is isomorphic to ℱ(c₀) for those K using a different method).

Kategorie tematyczne

• 46T99: None of the above, but in this section
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 226
• Numer: 3
• Strony: 213-227

Daty

wydano

2015

Twórcy

autor

Pedro Levit Kaufmann

• Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo, Campus São José dos Campos - Parque Tecnológico, Avenida Doutor Altino Bondensan, 500, 12247-016 São José dos Campos/SP, Brazil

Identyfikatory

DOI

10.4064/sm226-3-2