
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 $\ell_1(Γ)$, where $Γ=\text{dens}(M)$. If $\mathcal N$ is the 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 $\mathcal F(\mathcal N)$ is isomorphic to its $\ell_1$-sum. Finally, we prove that for all $X\cong C(K)$ spaces $\mathcal F(\mathcal N)$ are mutually isomorphic spaces with a Schauder basis.
Isomorphic theory (including renorming) of Banach spaces, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, uniformly discrete metric spaces, compact metric-spaces, Functional Analysis (math.FA), Lipschitz-free spaces, Mathematics - Functional Analysis, 46B10, Duality and reflexivity in normed linear and Banach spaces, approximation properties, FOS: Mathematics, 46B03, free Banach spaces, Schauder bases
Isomorphic theory (including renorming) of Banach spaces, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, uniformly discrete metric spaces, compact metric-spaces, Functional Analysis (math.FA), Lipschitz-free spaces, Mathematics - Functional Analysis, 46B10, Duality and reflexivity in normed linear and Banach spaces, approximation properties, FOS: Mathematics, 46B03, free Banach spaces, Schauder bases
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 15 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
