Approximation properties and Schauder decompositions in Lipschitz-free spaces

By G. Lancien, Eva Pernecká. 2012

56 citations recorded by the source corpus.

We prove that the Lipschitz-free space over a doubling metric space has the bounded approximation property. We also show that the Lipschitz-free spaces over $\ell_1^N$ or $\ell_1$ have monotone finite-dimensional Schauder decompositions.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f8bac046371685786648098c20cecc4f82c7380

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. A. Dalet
2. Pedro L. Kaufmann
3. G. Lancien
4. Gilles Godefroy
5. V. Zizler
6. P. Rueda
7. D. Achour

In Geometry and Topology

1. A. Dalet
2. Gilles Godefroy
3. Pedro L. Kaufmann
4. Enrique Alfonso Sánchez-Pérez
5. G. Lancien

In Mathematical Physics

1. A. Dalet
2. Gilles Godefroy
3. G. Lancien
4. Pedro L. Kaufmann
5. V. Zizler
6. Enrique Alfonso Sánchez-Pérez
7. P. Rueda
8. R. Yahi

Citations in the corpus

• On the structure of Lipschitz-free spaces (2015, unknown): “[8, 10, 12, 14, 15, 18, 20].”
• Free Spaces Over Some Proper Metric Spaces (2014, background): “[9] P. Hájek and E. Pernecká, Schauder bases in Lipschitz-free spaces, J. Math.”
• Products of Lipschitz-free spaces and applications (2014, background): “nach space X, Xhas the bounded approximation property if and only if F(X) has that property, and recently Hajek and Pernecka [4] have shown that F(Rn) admits a Schauder basis, rening a result from [10]. However, it is not known whether F(F) admits a Schauder basis for any given closed subset FˆRn. I”
• The non-linear geometry of Banach spaces after Nigel Kalton (2012, background): “So far, very little is known on this topic, which is related with the existence of linear extension operators for Lipschitz functions (see [15, 40, 68]).”
• Lipschitz operator ideals and the approximation property (2016, background): “Although in recent years there is an increasing interest for finding results on approximation properties related to Lipschitz functions and the free spaces Æ(X) of metric spaces X (see [15, 16, 21, 22, 29]), there are no explicit definitions of approximation properties on metric spaces.”