Some remarks on the structure of Lipschitz-free spaces

0476946 - MÚ 2018 RIV BE eng J - Journal Article
Hájek, Petr Pavel - Novotný, M.
Some remarks on the structure of Lipschitz-free spaces.
Bulletin of the Belgian Mathematical Society-Simon Stevin. Roč. 24, č. 2 (2017), s. 283-304. ISSN 1370-1444. E-ISSN 2034-1970
R&D Projects: GA ČR GA16-07378S
Institutional support: RVO:67985840
Keywords : free Banach spaces * compact metric-spaces * approximation properties
OECD category: Pure mathematics
Impact factor: 0.423, year: 2017
https://projecteuclid.org/euclid.bbms/1503453711

We give several structural results concerning the Lipschitz-free spaces F(M), where M is a metric space. We show that F(M) contains a complemented copy of l(1)(Gamma), where Gamma = dens(M). If N is a net in a finite dimensional Banach space X, we show that F(N) is isomorphic to its square. If X contains a complemented copy of l(p), c(0) then F(N) is isomorphic to its l(r)-sum. Finally, we prove that for all X congruent to C(K) spaces, where K is a metrizable compact, F(N) are mutually isomorphic spaces with a Schauder basis.
Permanent Link: http://hdl.handle.net/11104/0273352