Biduality and density in Lipschitz function spaces
| Autor: | Jiménez-Vargas, A., Sepulcre, J. M., Villegas-Vallecillos, Moisés |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | For pointed compact metric spaces $(X,d)$, we address the biduality problem as to when the space of Lipschitz functions $\mathrm{Lip}_0(X,d)$ is isometrically isomorphic to the bidual of the space of little Lipschitz functions $\mathrm{lip}_0(X,d)$, and show that this is the case whenever the closed unit ball of $\mathrm{lip}_0(X,d)$ is dense in the closed unit ball of $\mathrm{Lip}_0(X,d)$ with respect to the topology of pointwise convergence. Then we apply our density criterion to prove in an alternate way the real version of a classical result which asserts that $\mathrm{Lip}_0(X,d^\alpha)$ is isometrically isomorphic to $\mathrm{lip}_0(X,d^\alpha)^{**}$ for any $\alpha$ in $(0,1)$. Comment: 7 pages |
| Databáze: | arXiv |
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