Bulletin of the Belgian Mathematical Society - Simon Stevin

Some remarks on the structure of Lipschitz-free spaces

Peter Hájek and Matěj Novotný

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We give several structural results concerning the Lipschitz-free spaces $\mathcal F(M)$, where $M$ is a metric space. We show that $\mathcal F(M)$ contains a complemented copy of $\ell_1(\Gamma)$, where $\Gamma=\text{dens}(M)$. If $\mathcal N$ is a net in a finite dimensional Banach space $X$, we show that $\mathcal F(\mathcal N)$ is isomorphic to its square. If $X$ contains a complemented copy of $\ell_p, c_0$ then $\f(\mathcal N)$ is isomorphic to its$\ell_1$-sum. Finally, we prove that for all $X\cong C(K)$ spaces, where $K$ is a metrizable compact, $\f(\mathcal N)$ are mutually isomorphic spaces with a Schauder basis.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 2 (2017), 283-304.

First available in Project Euclid: 23 August 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B03: Isomorphic theory (including renorming) of Banach spaces 46B10: Duality and reflexivity [See also 46A25]


Hájek, Peter; Novotný, Matěj. Some remarks on the structure of Lipschitz-free spaces. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 2, 283--304. doi:10.36045/bbms/1503453711. https://projecteuclid.org/euclid.bbms/1503453711

Export citation