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april 2017 Some remarks on the structure of Lipschitz-free spaces
Peter Hájek, Matěj Novotný
Bull. Belg. Math. Soc. Simon Stevin 24(2): 283-304 (april 2017). DOI: 10.36045/bbms/1503453711

Abstract

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.

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Peter Hájek. Matěj Novotný. "Some remarks on the structure of Lipschitz-free spaces." Bull. Belg. Math. Soc. Simon Stevin 24 (2) 283 - 304, april 2017. https://doi.org/10.36045/bbms/1503453711

Information

Published: april 2017
First available in Project Euclid: 23 August 2017

zbMATH: 06850672
MathSciNet: MR3694004
Digital Object Identifier: 10.36045/bbms/1503453711

Subjects:
Primary: 46B03, 46B10

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 2 • april 2017
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