Isometric embedding of $\ell_1$ into Lipschitz-free spaces and $\ell_\infty$ into their duals
| Type of publication: | Article |
| Citation: | |
| Publication status: | Published |
| Journal: | Proc. Amer. Math. Soc. |
| Volume: | 145 |
| Year: | 2017 |
| Month: | August |
| Pages: | 3409-3421 |
| URL: | http://dx.doi.org/10.1090/proc... |
| DOI: | 10.1090/proc/13590 |
| Abstract: | We show that the dual of every infinite-dimensional Lipschitz-free Banach space contains an isometric copy of $\ell_\infty$ and that it is often the case that a Lipschitz-free Banach space contains a $1$-complemented subspace isometric to $\ell_1$. Even though we do not know whether the latter is true for every infinite-dimensional Lipschitz-free Banach space, we show that the space is never rotund. |
| Preprint year: | 2016 |
| Keywords: | |
| Authors | |
| Added by: | [mc] |
| Total mark: | 0 |
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